Graceful Labeling for Complete Bipartite Graphs

Size: px
Start display at page:

Download "Graceful Labeling for Complete Bipartite Graphs"

Transcription

1 Applied Mathematical Sciences, Vol. 8, 2014, no. 103, HIKARI Ltd, Graceful Labeling for Complete Bipartite Graphs V. J. Kaneria Department of Mathematics Saurashtra University, Rajkot , India H. M. Makadia Govt. Engineering College, Rajkot , India M. M. Jariya V. V. P. Engineering College, Rajkot , India Meera Meghapara Om Engineering College, Junagadh , India Copyright c 2014 V. J. Kaneria, H. M. Makadia, M. M. Jariya and Meera Meghapara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper contains some results on graceful labeling. We prove that the path union of complete bipartite graph and join sum of complete bipartite graphs are graceful. We also prove that star of complete bipartite graph is graceful. Mathematics Subject Classification: 05C78 Keywords: Complete bipartite graph, path union, join sum of graphs, star of a graph

2 5100 V. J. Kaneria, H. M. Makadia, M. M. Jariya and Meera Meghapara 1 Introduction : Let G = (V, E) be a simple, undirected and finite graph with p vertices and q edges. In this work K m,n denotes a complete bipartite graph. For all other terminology and notations we follows Harary (Harary 1972). We will give brief summary of definitions which are useful for this paper. Definition 1.1: A function f is called graceful labeling of a graph G = (V, E) if f : V {0, 1,..., q} is injective and the induce function f : E {1, 2,..., q} defined as f (e = uv) = f(u) f(v) is bijective, e = uv E. A graph G, which admits graceful labeling is called graceful graph. Definition 1.2: Let G be a graph and G 1, G 2,..., G n, n 2 be n copies of graph G. Then the graph obtained by adding an edge from G i to G i+1 (i = 1, 2,..., n 1) is called path union of G. Definition 1.3: Consider t copies of a graph G 0. Then graph G =< G (1) 0 ; G (2) 0 ;... ; G (t) 0 > obtained by joining two copies of the graph G (i) 0 and G (i+1) 0 by a vertex 1 i t 1 is called join sum of graphs. Definition 1.4: A graph obtained by replacing each vertex of star K 1,n by a graph G of n vertices is called star of G and it is denoted by G. The graph G which replaced at the center of K 1,n we call the central copy of G. For detail survey of graph labeling one can refer Gallian (Gallian 2013). Labeled graphs have many diversified applications. The graceful labeling was introduced by Rosa (Rosa 1967, p ). Golomb (Golomb 1972, p ) proved that the complete bipartite graph K m,n is graceful. Barrientos (Barrientos 2005, p ) proved that union of complete bipartite graphs is also graceful. Vaidya et al. (vaidya, Ghodasara, Sweta and Kaneria 2008, p ) introduced a star of a cycle and proved that it is cordial as well as 3 equitable graph. Kaneria and Makadia (Kaneria and Makadia 2012, p )proved that a star of a cycle C n (n 0 (mod 4)) is graceful. In present paper we introduced gracefulness of path union of complete bipartite graph, join sum of complete bipartite graphs and star of a complete bipartite graph. 2 Main Results : Theorem 2.1 : G =< K m1,n 1 ;... ; K mt,nt > the join sum of complete bipartite graphs is graceful, where m 1, n 1,..., m t, n t N. Proof : Let G be the join sum of complete bipartite graphs K m1,n 1,..., K mt,nt, where m 1, n 1,..., m t, n t N. Let u i,j (1 j m i ), v i,j (1 j n i ) be vertices of the complete bipartite graphs K mi,n i, i = 1, 2,..., t. Let w 1, w 2,..., w t 1 be vertices for join sum of the complete bipartite graphs and join vertices (u i,ni, w i ), (w i, u i+1,1 ), i = 1, 2,..., t 1 by an edge to produce join sum of complete bipartite graphs < K m1,n 1 ;... ; K mt,nt >.

3 Graceful labeling for complete bipartite graphs 5101 We define labeling function f : V {0, 1,..., q}, where q = Σ t i=1 m i n i + 2(t 1) as follows: f(u 1,i ) = i 1, i = 1, 2,..., m 1 f(v 1,i ) = q m 1 (i 1), i = 1, 2,..., n 1 and f(w j 1 ) = q Σ j 1 l=1 m l(n l 1) 2j + 3, f(u j,i ) = Σ j 1 l=1 m l + (i 1), i = 1, 2,..., m j f(v j,i ) = q Σ j 1 l=1 m l(n l 1) 2(j 1) m j (i 1), i = 1, 2,..., n j ; j = 2, 3,..., t. Above labeling pattern give rise graceful labeling to < K m1,n 1 ;... ; K mt,nt >. Illustration 2.2: G =< K 4,3 ; K 3,3 ; K 2,4 > and its graceful labeling shown in figure 1. Figure 1 Theorem 2.3 : Path union of complete bipartite graphs K m1,n 1,..., K mt,n t is graceful, where m 1, n 1,..., m t, n t N. Proof : Let G be a path union of complete bipartite graphs K m1,n 1,..., K mt,nt, where m 1, n 1,..., m t, n t N. To produce the path union of this graphs we join u i,mi with v i+1,1 by an edge, i = 1, 2,..., t 1, where u i,j (1 j m i ), v i,j (1 j n i ) are vertices of the complete bipartite graph K mi,n i, i = 1, 2,..., t. We define labeling function f : V m i n i + (t 1) as follows: {0, 1,..., q}, where q = Σ t i=1 f(u 1,i ) = i 1, i = 1, 2,..., m 1 f(v 1,i ) = q m 1 (i 1), i = 1, 2,..., n 1 f(u j,i ) = Σ j 1 l=1 m l + (i 1), i = 1, 2,..., m j f(v j,i ) = q Σ j 1 l=1 m l(n l 1) (j 1) m j (i 1), i = 1, 2,..., n j ; j = 2, 3,..., t. Above labeling pattern give rise graceful labeling to required graph.

4 5102 V. J. Kaneria, H. M. Makadia, M. M. Jariya and Meera Meghapara Illustration 2.4: Path union of K 3,2 ; K 4,3 ; K 1,4 and its graceful labeling shown in figure 2, in which edge labels are descending order at lower set of vertices. Figure 2 Theorem 2.5 : K m,n, the star of a complete bipartite graph is graceful. Proof : Let u 0,i (1 i m), v 0,j (1 j n) be vertices of central copy of Km,n and u l,i (1 i m), v l,j (1 j n) be vertices of other copies of K m,n, l = 1, 2,..., m + n. We define labeling function f : V {0, 1,..., q}, where q = (m + n + 1)mn + m + n as follows: f(u 0,i ) = i 1, i = 1, 2,..., m f(v 0,j ) = q (i 1)m, j = 1, 2,..., n f(u 1,i ) = q (mn + 1) + i, i = 1, 2,..., m f(v 1,i ) = jm, j = 1, 2,..., n f(u l,i ) = f(u l 2,i ) + (mn + 1), i = 1, 2,..., m f(v l,j ) = f(v l 2,j ) (mn + 1), j = 1, 2,..., n; l = 2, 3,..., m + n. Above defined labeling function f give rise edge labels 1, 2,..., mn, mn+ 2, mn + 3,..., 2mn + 1, 2mn + 3, 2mn + 4,..., 3mn + 2,..., (mn + 1)(m + n) + 1,..., q to all the copies of K m,n. To make Km,n as graceful graph mn + 1, 2(mn + 1),..., (m + n)(mn + 1) edge labels to be require. Now we see that the difference of vertex labels for the central copy K (0) m,n with its other copies K (i) m,n, 1 i m + n is precisely following sequence. (m + n)(mn + 1) mn + 1 (m + n 1)(mn + 1) 2(mn + 1)..

5 Graceful labeling for complete bipartite graphs 5103 ( m+n )(mn + 1), when m + n 0 (mod 2) 2 or )(mn + 1), when m + n 1 (mod 2) 2 ( m+n+1 )(mn + 1). 2 ( m+n 1 Using above sequence we can produce required edge labels by joining corresponding vertex of K m,n (0) with its other copies of K m,n, (i) i = 1, 2,..., m + n. Thus Km,n admits a graceful labeling and so it is a graceful graph. Illustration 2.6: K3,2 and its graceful labeling shown in figure 3. Figure 3 3 Concluding Remarks : We discussed here graceful labeling of some graphs obtained by complete bipartite graphs. Present work contributes three new results. Labeling pattern is demonstrated by means of illustrations, which provide better understanding of derived results. Acknowledgement: Authors of this paper would like to thanks reviewers for their valuable suggestions.

6 5104 V. J. Kaneria, H. M. Makadia, M. M. Jariya and Meera Meghapara References [1] C. Barrientos, The gracefulness of unions of cycles and complete bipartite graphs, J. Combin. Math. Combin. Comput. 52 (2005), [2] J. A. Gallian, The Electronics Journal of Combinatorics, 19, DS6(2013). [3] S. W. Golomb, How to number a graph, in Graph Theory and Computing, R. C. Read, ed., Academic Press, New York, (1972) [4] F. Harary, Graph theory Addition Wesley, Massachusetts, [5] V. J. Kaneria and H. M. Makadia, Some Graceful Graphs J. of Math. Research, 4 (1), (2012) [6] A. Rosa, On certain valuation of graph, Theory of Graphs (Rome, July 1966), Goden and Breach, N. Y. and Paris, 1967, [7] S. K. Vaidya, G. V. Ghodasara, Sweta Srivastav and V. J. Kaneria Cordial and 3 equitable labeling of Star of a Cycle, Mathematics Today, 24 (2008), Received: June 7, 2014

Graceful Related Labeling and its Applications

Graceful Related Labeling and its Applications International Journal of Mathematics Research (IJMR). ISSN 0976-5840 Volume 7, Number 1 (015), pp. 47 54 International Research Publication House http://www.irphouse.com Graceful Related Labeling and its

More information

SQUARE DIFFERENCE 3-EQUITABLE LABELING FOR SOME GRAPHS. Sattur , TN, India. Sattur , TN, India.

SQUARE DIFFERENCE 3-EQUITABLE LABELING FOR SOME GRAPHS. Sattur , TN, India. Sattur , TN, India. International Journal of Science, Engineering Technology Research (IJSETR), Volume 5, Issue, March 2016 SQUARE DIFFERENCE -EQUITABLE LABELING FOR SOME GRAPHS R Loheswari 1 S Saravana kumar 2 1 Research

More information

ROOT SQUARE MEAN GRAPHS OF ORDER 5

ROOT SQUARE MEAN GRAPHS OF ORDER 5 Available online at http://scik.org J. Math. Comput. Sci. 5 (2015), No. 5, 708-715 ISSN: 1927-5307 ROOT SQUARE MEAN GRAPHS OF ORDER 5 S.S. SANDHYA 1 S. SOMASUNDARAM 2 AND S. ANUSA 3,* 1 Department of Mathematics,

More information

Root Square Mean Labeling of Some More. Disconnected Graphs

Root Square Mean Labeling of Some More. Disconnected Graphs International Mathematical Forum, Vol. 10, 2015, no. 1, 25-34 HIKARI Ltd,www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.411196 Root Square Mean Labeling of Some More Disconnected Graphs S. S. Sandhya

More information

Odd-even sum labeling of some graphs

Odd-even sum labeling of some graphs International Journal of Mathematics and Soft Computing Vol.7, No.1 (017), 57-63. ISSN Print : 49-338 Odd-even sum labeling of some graphs ISSN Online : 319-515 K. Monika 1, K. Murugan 1 Department of

More information

Difference Cordial Labeling of Graphs Obtained from Double Snakes

Difference Cordial Labeling of Graphs Obtained from Double Snakes International Journal of Mathematics Research. ISSN 0976-5840 Volume 5, Number 3 (013), pp. 317-3 International Research Publication House http://www.irphouse.com Difference Cordial Labeling of Graphs

More information

Prime Cordial Labeling For Some Cycle Related Graphs

Prime Cordial Labeling For Some Cycle Related Graphs Int. J. Open Probles Copt. Math., Vol. 3, No. 5, Deceber 010 ISSN 1998-66; Copyright c ICSRS Publication, 010 www.i-csrs.org Prie Cordial Labeling For Soe Cycle Related Graphs S K Vaidya 1 and P L Vihol

More information

On the Gracefulness of Cycle related graphs

On the Gracefulness of Cycle related graphs Volume 117 No. 15 017, 589-598 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu On the Gracefulness of Cycle related graphs S.Venkatesh 1 and S. Sivagurunathan

More information

Graceful Labeling of Some Theta Related Graphs

Graceful Labeling of Some Theta Related Graphs Intern. J. Fuzzy Mathematical Archive Vol. 2, 2013, 78-84 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 11 September 2013 www.researchmathsci.org International Journal of Graceful Labeling of Some

More information

ODD HARMONIOUS LABELING OF PLUS GRAPHS

ODD HARMONIOUS LABELING OF PLUS GRAPHS BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 303-4874, ISSN (o) 303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 7(017), 515-56 DOI: 10.751/BIMVI1703515J Former BULLETIN OF THE

More information

k-difference cordial labeling of graphs

k-difference cordial labeling of graphs International J.Math. Combin. Vol.(016), 11-11 k-difference cordial labeling of graphs R.Ponraj 1, M.Maria Adaickalam and R.Kala 1.Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-6741,

More information

Sum divisor cordial labeling for star and ladder related graphs

Sum divisor cordial labeling for star and ladder related graphs Proyecciones Journal of Mathematics Vol. 35, N o 4, pp. 437-455, December 016. Universidad Católica del Norte Antofagasta - Chile Sum divisor cordial labeling for star and ladder related graphs A. Lourdusamy

More information

Further results on relaxed mean labeling

Further results on relaxed mean labeling Int. J. Adv. Appl. Math. and Mech. 3(3) (016) 9 99 (ISSN: 347-59) Journal homepage: www.ijaamm.com IJAAMM International Journal of Advances in Applied Mathematics and Mechanics Further results on relaxed

More information

Skolem Difference Mean Graphs

Skolem Difference Mean Graphs royecciones Journal of Mathematics Vol. 34, N o 3, pp. 43-54, September 015. Universidad Católica del Norte Antofagasta - Chile Skolem Difference Mean Graphs M. Selvi D. Ramya Dr. Sivanthi Aditanar College

More information

Magic Graphoidal on Class of Trees A. Nellai Murugan

Magic Graphoidal on Class of Trees A. Nellai Murugan Bulletin of Mathematical Sciences and Applications Online: 2014-08-04 ISSN: 2278-9634, Vol. 9, pp 33-44 doi:10.18052/www.scipress.com/bmsa.9.33 2014 SciPress Ltd., Switzerland Magic Graphoidal on Class

More information

SOME EXTENSION OF 1-NEAR MEAN CORDIAL LABELING OF GRAPHS. Sattur , TN, India.

SOME EXTENSION OF 1-NEAR MEAN CORDIAL LABELING OF GRAPHS. Sattur , TN, India. SOME EXTENSION OF 1-NEAR MEAN CORDIAL LABELING OF GRAPHS A.Raja Rajeswari 1 and S.Saravana Kumar 1 Research Scholar, Department of Mathematics, Sri S.R.N.M.College, Sattur-66 03, TN, India. Department

More information

Further Studies on the Sparing Number of Graphs

Further Studies on the Sparing Number of Graphs Further Studies on the Sparing Number of Graphs N K Sudev 1, and K A Germina 1 Department of Mathematics arxiv:1408.3074v1 [math.co] 13 Aug 014 Vidya Academy of Science & Technology Thalakkottukara, Thrissur

More information

Double Total Domination on Generalized Petersen Graphs 1

Double Total Domination on Generalized Petersen Graphs 1 Applied Mathematical Sciences, Vol. 11, 2017, no. 19, 905-912 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.7114 Double Total Domination on Generalized Petersen Graphs 1 Chengye Zhao 2

More information

Power Mean Labeling of Identification Graphs

Power Mean Labeling of Identification Graphs International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 6, Issue, 208, PP -6 ISSN 2347-307X (Print) & ISSN 2347-342 (Online) DOI: http://dx.doi.org/0.2043/2347-342.06000

More information

Available Online through

Available Online through ISSN: 0975-766X CODEN: IJPTFI Available Online through Research Article www.ijptonline.com 0-EDGE MAGIC LABELING OF SHADOW GRAPH J.Jayapriya*, Department of Mathematics, Sathyabama University, Chennai-119,

More information

Odd Sum Labeling of Tree Related Graphs

Odd Sum Labeling of Tree Related Graphs International Journal of Mathematics And its Applications Volume 4, Issue 4 (016), 11 16. ISSN: 347-1557 Available Online: http://ijmaa.in/ International Journal 347-1557 of Mathematics Applications And

More information

Restrained Independent 2-Domination in the Join and Corona of Graphs

Restrained Independent 2-Domination in the Join and Corona of Graphs Applied Mathematical Sciences, Vol. 11, 2017, no. 64, 3171-3176 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.711343 Restrained Independent 2-Domination in the Join and Corona of Graphs

More information

On (k, d)-multiplicatively indexable graphs

On (k, d)-multiplicatively indexable graphs Chapter 3 On (k, d)-multiplicatively indexable graphs A (p, q)-graph G is said to be a (k,d)-multiplicatively indexable graph if there exist an injection f : V (G) N such that the induced function f :

More information

The Rainbow Connection of Windmill and Corona Graph

The Rainbow Connection of Windmill and Corona Graph Applied Mathematical Sciences, Vol. 8, 2014, no. 128, 6367-6372 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.48632 The Rainbow Connection of Windmill and Corona Graph Yixiao Liu Department

More information

Research Article Some New Results on Prime Cordial Labeling

Research Article Some New Results on Prime Cordial Labeling ISRN Combinatorics Volume 014, Article ID 07018, 9 pages http://dx.doi.org/10.1155/014/07018 Research Article Some New Results on Prime Cordial Labeling S. K. Vaidya 1 andn.h.shah 1 Saurashtra University,

More information

On Graceful Labeling of Some Bicyclic Graphs

On Graceful Labeling of Some Bicyclic Graphs Intern. J. Fuzzy Mathematical Archive Vol. 3, 2013, 1-8 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 4 October 2013 www.researchmathsci.org International Journal of On Graceful Labeling of Some

More information

Strong Integer Additive Set-valued Graphs: A Creative Review

Strong Integer Additive Set-valued Graphs: A Creative Review Strong Integer Additive Set-valued Graphs: A Creative Review N. K. Sudev arxiv:1504.07132v1 [math.gm] 23 Apr 2015 Department of Mathematics Vidya Academy of Science & Technology Thalakkottukara, Thrissur-680501,

More information

Secure Weakly Convex Domination in Graphs

Secure Weakly Convex Domination in Graphs Applied Mathematical Sciences, Vol 9, 2015, no 3, 143-147 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ams2015411992 Secure Weakly Convex Domination in Graphs Rene E Leonida Mathematics Department

More information

Super Fibonacci Graceful Labeling

Super Fibonacci Graceful Labeling International J.Math. Combin. Vol. (010), -40 Super Fibonacci Graceful Labeling R. Sridevi 1, S.Navaneethakrishnan and K.Nagarajan 1 1. Department of Mathematics, Sri S.R.N.M.College, Sattur - 66 0, Tamil

More information

SUPER MEAN NUMBER OF A GRAPH

SUPER MEAN NUMBER OF A GRAPH Kragujevac Journal of Mathematics Volume Number (0), Pages 9 0. SUPER MEAN NUMBER OF A GRAPH A. NAGARAJAN, R. VASUKI, AND S. AROCKIARAJ Abstract. Let G be a graph and let f : V (G) {,,..., n} be a function

More information

A Creative Review on Integer Additive Set-Valued Graphs

A Creative Review on Integer Additive Set-Valued Graphs A Creative Review on Integer Additive Set-Valued Graphs N. K. Sudev arxiv:1407.7208v2 [math.co] 30 Jan 2015 Department of Mathematics Vidya Academy of Science & Technology Thalakkottukara, Thrissur-680501,

More information

Restrained Weakly Connected Independent Domination in the Corona and Composition of Graphs

Restrained Weakly Connected Independent Domination in the Corona and Composition of Graphs Applied Mathematical Sciences, Vol. 9, 2015, no. 20, 973-978 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121046 Restrained Weakly Connected Independent Domination in the Corona and

More information

On Odd Sum Graphs. S.Arockiaraj. Department of Mathematics. Mepco Schlenk Engineering College, Sivakasi , Tamilnadu, India. P.

On Odd Sum Graphs. S.Arockiaraj. Department of Mathematics. Mepco Schlenk Engineering College, Sivakasi , Tamilnadu, India. P. International J.Math. Combin. Vol.4(0), -8 On Odd Sum Graphs S.Arockiaraj Department of Mathematics Mepco Schlenk Engineering College, Sivakasi - 66 00, Tamilnadu, India P.Mahalakshmi Department of Mathematics

More information

A Study on Integer Additive Set-Graceful Graphs

A Study on Integer Additive Set-Graceful Graphs A Study on Integer Additive Set-Graceful Graphs N. K. Sudev arxiv:1403.3984v3 [math.co] 27 Sep 2015 Department of Mathematics Vidya Academy of Science & Technology Thalakkottukara, Thrissur, India. E-mail:

More information

One Modulo Three Harmonic Mean Labeling of Graphs

One Modulo Three Harmonic Mean Labeling of Graphs International Journal of Mathematics Research. ISSN 0976-5840 Volume 5, Number 4 (20), pp. 4-422 International Research Publication House http://www.irphouse.com One Modulo Three Harmonic Mean Labeling

More information

Independent Transversal Equitable Domination in Graphs

Independent Transversal Equitable Domination in Graphs International Mathematical Forum, Vol. 8, 2013, no. 15, 743-751 HIKARI Ltd, www.m-hikari.com Independent Transversal Equitable Domination in Graphs Dhananjaya Murthy B. V 1, G. Deepak 1 and N. D. Soner

More information

Decompositions of Balanced Complete Bipartite Graphs into Suns and Stars

Decompositions of Balanced Complete Bipartite Graphs into Suns and Stars International Journal of Contemporary Mathematical Sciences Vol. 13, 2018, no. 3, 141-148 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2018.8515 Decompositions of Balanced Complete Bipartite

More information

Super Mean Labeling of Some Classes of Graphs

Super Mean Labeling of Some Classes of Graphs International J.Math. Combin. Vol.1(01), 83-91 Super Mean Labeling of Some Classes of Graphs P.Jeyanthi Department of Mathematics, Govindammal Aditanar College for Women Tiruchendur-68 15, Tamil Nadu,

More information

Further Results on Square Sum Graph

Further Results on Square Sum Graph International Mathematical Forum, Vol. 8, 2013, no. 1, 47-57 Further Results on Square Sum Graph K. A. Germina School of Mathematical and Physical Sciences Central University of Kerala, Kasaragode, India

More information

Graceful Tree Conjecture for Infinite Trees

Graceful Tree Conjecture for Infinite Trees Graceful Tree Conjecture for Infinite Trees Tsz Lung Chan Department of Mathematics The University of Hong Kong, Pokfulam, Hong Kong h0592107@graduate.hku.hk Wai Shun Cheung Department of Mathematics The

More information

Edge Fixed Steiner Number of a Graph

Edge Fixed Steiner Number of a Graph International Journal of Mathematical Analysis Vol. 11, 2017, no. 16, 771-785 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.7694 Edge Fixed Steiner Number of a Graph M. Perumalsamy 1,

More information

Induced Cycle Decomposition of Graphs

Induced Cycle Decomposition of Graphs Applied Mathematical Sciences, Vol. 9, 2015, no. 84, 4165-4169 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.5269 Induced Cycle Decomposition of Graphs Rosalio G. Artes, Jr. Department

More information

Topological Integer Additive Set-Graceful Graphs

Topological Integer Additive Set-Graceful Graphs Topological Integer Additive Set-Graceful Graphs N. K.Sudev arxiv:1506.01240v1 [math.gm] 3 Jun 2015 Department of Mathematics, Vidya Academy of Science & Technology, Thalakkottukara, Thrissur - 680501,

More information

The Exquisite Integer Additive Set-Labeling of Graphs

The Exquisite Integer Additive Set-Labeling of Graphs The Exquisite Integer Additive Set-Labeling of Graphs N. K. Sudev 1, K. A. Germina 2 Department of Mathematics, Vidya Academy of Science & Technology, Thalakkottukara, Thrissur - 680501, Kerala, India.

More information

Super Fibonacci Graceful Labeling of Some Special Class of Graphs

Super Fibonacci Graceful Labeling of Some Special Class of Graphs International J.Math. Combin. Vol.1 (2011), 59-72 Super Fibonacci Graceful Labeling of Some Special Class of Graphs R.Sridevi 1, S.Navaneethakrishnan 2 and K.Nagarajan 1 1. Department of Mathematics, Sri

More information

More on Tree Cover of Graphs

More on Tree Cover of Graphs International Journal of Mathematical Analysis Vol. 9, 2015, no. 12, 575-579 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.410320 More on Tree Cover of Graphs Rosalio G. Artes, Jr.

More information

Combinatorial Labelings Of Graphs

Combinatorial Labelings Of Graphs Applied Mathematics E-Notes, 6(006), 51-58 c ISSN 1607-510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Combinatorial Labelings Of Graphs Suresh Manjanath Hegde, Sudhakar Shetty

More information

Secure Weakly Connected Domination in the Join of Graphs

Secure Weakly Connected Domination in the Join of Graphs International Journal of Mathematical Analysis Vol. 9, 2015, no. 14, 697-702 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.519 Secure Weakly Connected Domination in the Join of Graphs

More information

Locating Chromatic Number of Banana Tree

Locating Chromatic Number of Banana Tree International Mathematical Forum, Vol. 12, 2017, no. 1, 39-45 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.610138 Locating Chromatic Number of Banana Tree Asmiati Department of Mathematics

More information

Strong Integer Additive Set-valued Graphs: A Creative Review

Strong Integer Additive Set-valued Graphs: A Creative Review Strong Integer Additive Set-valued Graphs: A Creative Review N. K. Sudev Department of Mathematics Vidya Academy of Science & Technology Thalakkottukara, Thrissur-680501, India. K. A. Germina PG & Research

More information

SUPER ROOT SQUARE MEAN LABELING OF SOME NEW GRAPHS

SUPER ROOT SQUARE MEAN LABELING OF SOME NEW GRAPHS SUPER ROOT SQUARE MEAN LABELING OF SOME NEW GRAPHS 1 S.S.Sandhya S.Somasundaram and 3 S.Anusa 1.Department of Mathematics,Sree Ayyappa College for women,chunkankadai:69003,.department of Mathematics, Manonmaniam

More information

Double Total Domination in Circulant Graphs 1

Double Total Domination in Circulant Graphs 1 Applied Mathematical Sciences, Vol. 12, 2018, no. 32, 1623-1633 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.811172 Double Total Domination in Circulant Graphs 1 Qin Zhang and Chengye

More information

Even Star Decomposition of Complete Bipartite Graphs

Even Star Decomposition of Complete Bipartite Graphs Journal of Mathematics Research; Vol. 8, No. 5; October 2016 ISSN 1916-9795 E-ISSN 1916-9809 Published by Canadian Center of Science and Education Even Star Decomposition of Complete Bipartite Graphs E.

More information

H Paths in 2 Colored Tournaments

H Paths in 2 Colored Tournaments International Journal of Contemporary Mathematical Sciences Vol. 10, 2015, no. 5, 185-195 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2015.5418 H Paths in 2 Colo Tournaments Alejandro

More information

Rainbow Connection Number of the Thorn Graph

Rainbow Connection Number of the Thorn Graph Applied Mathematical Sciences, Vol. 8, 2014, no. 128, 6373-6377 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.48633 Rainbow Connection Number of the Thorn Graph Yixiao Liu Department

More information

Hyperbolic Functions and. the Heat Balance Integral Method

Hyperbolic Functions and. the Heat Balance Integral Method Nonl. Analysis and Differential Equations, Vol. 1, 2013, no. 1, 23-27 HIKARI Ltd, www.m-hikari.com Hyperbolic Functions and the Heat Balance Integral Method G. Nhawu and G. Tapedzesa Department of Mathematics,

More information

Some New Results on Super Stolarsky-3 Mean Labeling of Graphs

Some New Results on Super Stolarsky-3 Mean Labeling of Graphs International Journal of Mathematics Research. ISSN 0976-5840 Volume 10, Number 1 (2018), pp. 7-20 International Research Publication House http://www.irphouse.com Some New Results on Super Stolarsky-3

More information

Distance Two Labeling of Some Total Graphs

Distance Two Labeling of Some Total Graphs Gen. Math. Notes, Vol. 3, No. 1, March 2011, pp.100-107 ISSN 2219-7184; Copyright c ICSRS Publication, 2011 www.i-csrs.org Available free online at http://www.geman.in Distance Two Labeling of Some Total

More information

On Pairs of Disjoint Dominating Sets in a Graph

On Pairs of Disjoint Dominating Sets in a Graph International Journal of Mathematical Analysis Vol 10, 2016, no 13, 623-637 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ijma20166343 On Pairs of Disjoint Dominating Sets in a Graph Edward M Kiunisala

More information

On a 3-Uniform Path-Hypergraph on 5 Vertices

On a 3-Uniform Path-Hypergraph on 5 Vertices Applied Mathematical Sciences, Vol. 10, 2016, no. 30, 1489-1500 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.512742 On a 3-Uniform Path-Hypergraph on 5 Vertices Paola Bonacini Department

More information

UNIVERSITÀ DEGLI STUDI DI ROMA LA SAPIENZA

UNIVERSITÀ DEGLI STUDI DI ROMA LA SAPIENZA UNIVERSITÀ DEGLI STUDI DI ROMA LA SAPIENZA On d-graceful labelings Anita Pasotti Quaderni Elettronici del Seminario di Geometria Combinatoria 7E (Maggio 0) http://wwwmatuniromait/~combinat/quaderni Dipartimento

More information

One Modulo Three Root Square Mean Labeling of Some Disconnected Graphs

One Modulo Three Root Square Mean Labeling of Some Disconnected Graphs Annals of Pure and Applied Mathematics Vol. 6, No. 2, 208, 255-263 ISSN: 2279-087X (P), 2279-0888(online) Published on February 208 www.researchmathsci.org DOI: http://dx.doi.org/0.2257/apam.v6n2a Annals

More information

Note on Strong Roman Domination in Graphs

Note on Strong Roman Domination in Graphs Applied Mathematical Sciences, Vol. 12, 2018, no. 11, 55-541 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.851 Note on Strong Roman Domination in Graphs Jiaxue Xu and Zhiping Wang Department

More information

Devaney's Chaos of One Parameter Family. of Semi-triangular Maps

Devaney's Chaos of One Parameter Family. of Semi-triangular Maps International Mathematical Forum, Vol. 8, 2013, no. 29, 1439-1444 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.36114 Devaney's Chaos of One Parameter Family of Semi-triangular Maps

More information

Super Root Square Mean Labeling Of Disconnected Graphs

Super Root Square Mean Labeling Of Disconnected Graphs International Journal of Mathematics And its Applications Volume 4, Issue 1 C (2016), 93 98. ISSN: 2347-1557 Available Online: http://ijmaa.in/ International Journal 2347-1557 of Mathematics Applications

More information

Morphisms Between the Groups of Semi Magic Squares and Real Numbers

Morphisms Between the Groups of Semi Magic Squares and Real Numbers International Journal of Algebra, Vol. 8, 2014, no. 19, 903-907 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2014.212137 Morphisms Between the Groups of Semi Magic Squares and Real Numbers

More information

Direct Product of BF-Algebras

Direct Product of BF-Algebras International Journal of Algebra, Vol. 10, 2016, no. 3, 125-132 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.614 Direct Product of BF-Algebras Randy C. Teves and Joemar C. Endam Department

More information

On the Union of Graphs Ramsey Numbers

On the Union of Graphs Ramsey Numbers Applied Mathematical Sciences, Vol. 8, 2014, no. 16, 767-773 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.311641 On the Union of Graphs Ramsey Numbers I Wayan Sudarsana Combinatorial

More information

β Baire Spaces and β Baire Property

β Baire Spaces and β Baire Property International Journal of Contemporary Mathematical Sciences Vol. 11, 2016, no. 5, 211-216 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2016.612 β Baire Spaces and β Baire Property Tugba

More information

Harmonic Mean Labeling for Some Special Graphs

Harmonic Mean Labeling for Some Special Graphs International Journal of Mathematics Research. ISSN 0976-5840 Volume 5, Number 1 (2013), pp. 55-64 International Research Publication House http://www.irphouse.com Harmonic Mean Labeling for Some Special

More information

International Mathematical Forum, Vol. 9, 2014, no. 36, HIKARI Ltd,

International Mathematical Forum, Vol. 9, 2014, no. 36, HIKARI Ltd, International Mathematical Forum, Vol. 9, 2014, no. 36, 1751-1756 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.411187 Generalized Filters S. Palaniammal Department of Mathematics Thiruvalluvar

More information

ON SET-INDEXERS OF GRAPHS

ON SET-INDEXERS OF GRAPHS Palestine Journal of Mathematics Vol. 3(2) (2014), 273 280 Palestine Polytechnic University-PPU 2014 ON SET-INDEXERS OF GRAPHS Ullas Thomas and Sunil C Mathew Communicated by Ayman Badawi MSC 2010 Classification:

More information

Super edge-magic labeling of graphs: deficiency and maximality

Super edge-magic labeling of graphs: deficiency and maximality Electronic Journal of Graph Theory and Applications 5 () (017), 1 0 Super edge-magic labeling of graphs: deficiency and maximality Anak Agung Gede Ngurah a, Rinovia Simanjuntak b a Department of Civil

More information

IN this paper we consider simple, finite, connected and

IN this paper we consider simple, finite, connected and INTERNATIONAL JOURNAL OF MATHEMATICS AND SCIENTIFIC COMPUTING (ISSN: -5), VOL., NO., -Eqitable Labeling for Some Star and Bistar Related Graphs S.K. Vaidya and N.H. Shah Abstract In this paper we proe

More information

Contra θ-c-continuous Functions

Contra θ-c-continuous Functions International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 1, 43-50 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.714 Contra θ-c-continuous Functions C. W. Baker

More information

Some Results on Super Mean Graphs

Some Results on Super Mean Graphs International J.Math. Combin. Vol.3 (009), 8-96 Some Results on Super Mean Graphs R. Vasuki 1 and A. Nagarajan 1 Department of Mathematics, Dr.Sivanthi Aditanar College of Engineering, Tiruchendur - 68

More information

Graceful polynomials of small degree

Graceful polynomials of small degree Graceful polynomials of small degree Andrea Vietri 1 1 Dipartimento di Scienze di Base e Applicate per l Ingegneria Sapienza Università di Roma WAGTCN2018, Naples, 13-14 September 2018 Andrea Vietri 1

More information

Solving Homogeneous Systems with Sub-matrices

Solving Homogeneous Systems with Sub-matrices Pure Mathematical Sciences, Vol 7, 218, no 1, 11-18 HIKARI Ltd, wwwm-hikaricom https://doiorg/112988/pms218843 Solving Homogeneous Systems with Sub-matrices Massoud Malek Mathematics, California State

More information

New Constructions of Antimagic Graph Labeling

New Constructions of Antimagic Graph Labeling New Constructions of Antimagic Graph Labeling Tao-Ming Wang and Cheng-Chih Hsiao Department of Mathematics Tunghai University, Taichung, Taiwan wang@thu.edu.tw Abstract An anti-magic labeling of a finite

More information

Secure Connected Domination in a Graph

Secure Connected Domination in a Graph International Journal of Mathematical Analysis Vol. 8, 2014, no. 42, 2065-2074 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.47221 Secure Connected Domination in a Graph Amerkhan G.

More information

L(2,1)-Labeling: An Algorithmic Approach to Cycle Dominated Graphs

L(2,1)-Labeling: An Algorithmic Approach to Cycle Dominated Graphs MATEMATIKA, 2014, Volume 30, Number 2, 109-116 c UTM Centre for Industrial and Applied Mathematics L(2,1)-Labeling: An Algorithmic Approach to Cycle Dominated Graphs Murugan Muthali Tamil Nadu Open University

More information

Some Properties of D-sets of a Group 1

Some Properties of D-sets of a Group 1 International Mathematical Forum, Vol. 9, 2014, no. 21, 1035-1040 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.45104 Some Properties of D-sets of a Group 1 Joris N. Buloron, Cristopher

More information

Maximal Square Sum Subgraph of a Complete Graph

Maximal Square Sum Subgraph of a Complete Graph International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 2, Issue 1, January - 2014, PP 108-115 ISSN 2347-307X (Print) & ISSN 2347-3142 (Online) www.arcjournals.org Maximal

More information

International Journal of Scientific Research and Reviews

International Journal of Scientific Research and Reviews Research article Available online www.ijsrr.org ISSN: 2279 0543 International Journal of Scientific Research and Reviews Fibonacci Prime Labeling of Udukkai and Octopus Graphs Chandrakala S. *1 and Sekar

More information

Elegant Labeled Graphs

Elegant Labeled Graphs Journal of Informatics and Mathematical Sciences Volume 2, Number 1 (2010), pp. 45 49 RGN Publications http://www.rgnpublications.com Elegant Labeled Graphs A. Elumalai and G. Sethuraman Abstract. An elegant

More information

Equiblocking Sets in K 2,2 -Designs and in K 3,3 -Designs

Equiblocking Sets in K 2,2 -Designs and in K 3,3 -Designs Applied Mathematical Sciences, Vol. 7, 013, no. 91, 4549-4557 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.013.36341 Equiblocking Sets in K, -Designs and in K 3,3 -Designs Mario Gionfriddo

More information

Regular Generalized Star b-continuous Functions in a Bigeneralized Topological Space

Regular Generalized Star b-continuous Functions in a Bigeneralized Topological Space International Journal of Mathematical Analysis Vol. 9, 2015, no. 16, 805-815 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.5230 Regular Generalized Star b-continuous Functions in a

More information

Pyramidal Sum Labeling In Graphs

Pyramidal Sum Labeling In Graphs ISSN : 48-96, Vol 8, Issue 4, ( Part -I) April 8, pp-9 RESEARCH ARTICLE Pyramidal Sum Labeling In Graphs OPEN ACCESS HVelet Getzimah, D S T Ramesh ( department Of Mathematics, Pope s College, Sayerpuram-68,Ms

More information

Mean Cordial Labeling of Tadpole and Olive Tree

Mean Cordial Labeling of Tadpole and Olive Tree Annals of Pure and Applied Mathematics Vol. 11, No. 2, 216, 19-116 ISSN: 2279-87X (P), 2279-888(online) Published on 8 June 216 www.researchmathsci.org Annals of Mean Cordial Labeling of Tadpole and Olive

More information

Mappings of the Direct Product of B-algebras

Mappings of the Direct Product of B-algebras International Journal of Algebra, Vol. 10, 2016, no. 3, 133-140 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.615 Mappings of the Direct Product of B-algebras Jacel Angeline V. Lingcong

More information

Approximations to the t Distribution

Approximations to the t Distribution Applied Mathematical Sciences, Vol. 9, 2015, no. 49, 2445-2449 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.52148 Approximations to the t Distribution Bashar Zogheib 1 and Ali Elsaheli

More information

On a Certain Representation in the Pairs of Normed Spaces

On a Certain Representation in the Pairs of Normed Spaces Applied Mathematical Sciences, Vol. 12, 2018, no. 3, 115-119 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.712362 On a Certain Representation in the Pairs of ormed Spaces Ahiro Hoshida

More information

Double domination in signed graphs

Double domination in signed graphs PURE MATHEMATICS RESEARCH ARTICLE Double domination in signed graphs P.K. Ashraf 1 * and K.A. Germina 2 Received: 06 March 2016 Accepted: 21 April 2016 Published: 25 July 2016 *Corresponding author: P.K.

More information

Fuzzy Sequences in Metric Spaces

Fuzzy Sequences in Metric Spaces Int. Journal of Math. Analysis, Vol. 8, 2014, no. 15, 699-706 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4262 Fuzzy Sequences in Metric Spaces M. Muthukumari Research scholar, V.O.C.

More information

A Direct Proof of Caristi s Fixed Point Theorem

A Direct Proof of Caristi s Fixed Point Theorem Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289-2294 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.66190 A Direct Proof of Caristi s Fixed Point Theorem Wei-Shih Du Department

More information

Diameter of the Zero Divisor Graph of Semiring of Matrices over Boolean Semiring

Diameter of the Zero Divisor Graph of Semiring of Matrices over Boolean Semiring International Mathematical Forum, Vol. 9, 2014, no. 29, 1369-1375 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.47131 Diameter of the Zero Divisor Graph of Semiring of Matrices over

More information

-Complement of Intuitionistic. Fuzzy Graph Structure

-Complement of Intuitionistic. Fuzzy Graph Structure International Mathematical Forum, Vol. 12, 2017, no. 5, 241-250 HIKRI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.612171 -Complement of Intuitionistic Fuzzy Graph Structure Vandana ansal Department

More information

Integral Root Labeling of Graphs 1 V.L. Stella Arputha Mary & 2 N. Nanthini

Integral Root Labeling of Graphs 1 V.L. Stella Arputha Mary & 2 N. Nanthini International Journal of Mathematics Trends and Technology (IJMTT) Volume Number - February 08 Integral Root Labeling of Graphs V.L. Stella Arputha Mary & N. Nanthini Department of Mathematics, St. Mary

More information

Locating-Dominating Sets in Graphs

Locating-Dominating Sets in Graphs Applied Mathematical Sciences, Vol. 8, 2014, no. 88, 4381-4388 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.46400 Locating-Dominating Sets in Graphs Sergio R. Canoy, Jr. 1, Gina A.

More information