Restrained Weakly Connected Independent Domination in the Corona and Composition of Graphs
|
|
- Victoria Melton
- 5 years ago
- Views:
Transcription
1 Applied Mathematical Sciences, Vol. 9, 2015, no. 20, HIKARI Ltd, Restrained Weakly Connected Independent Domination in the Corona and Composition of Graphs Rene E. Leonida Mathematics Department College of Natural Sciences and Mathematics Mindanao State University Fatima, General Santos City, Philippines Copyright c 2015 Rene E. Leonida. 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 In this paper, we explore the concept of restrained weakly connected independent domination in graphs. In particular, we characterized the restrained weakly connected independent dominating sets in the corona, and composition of graphs and; as a consequence, their restrained weakly connected independent domination numbers are obtained. Mathematics Subject Classification: 05C69 Keywords: domination, restrained domination, independent domination, weakly connected domination, restrained weakly connected independent domination 1 Introduction and Preliminary Results Let G = (V (G), E(G)) be a simple connected graph. For any vertex v V (G), the open neighborhood of v is the set N(v) = {u V (G) : uv E(G)} and the closed neighborhood of v is the set N[v] = N(v) {v}. For a set X V (G), the open neighborhood of X is N(X) = v X N(v) and the closed neighborhood of X is N[X] = X N(X). A subset S of V (G) is an
2 974 Rene E. Leonida independent set if for every x, y S, xy / E(G). The independence number β(g) of G is the largest cardinality of an independent set of G. A subset S of V (G) is called weakly connected if the subgraph S w = (N G [S], E W ) weakly induced by S, is connected, where E W is the set of all edges with at least one vertex in S. A subset S of V (G) is a dominating set of G if for every v V (G)\S, there exists u S such that uv E(G). The domination number γ(g) of G is the smallest cardinality of a dominating set of G. A dominating set of G which is independent is called an independent dominating set of G. The independent domination number i(g) of G is the smallest cardinality of an independent dominating set of G. A dominating set of G which is weakly connected is called a weakly connected dominating set. The weakly connected domination number γ w (G) of G is the smallest cardinality of a weakly connected dominating set of G. An independent dominating set of G which is weakly connected is called a weakly connected independent dominating set. The weakly connected independent domination number i w (G) of G is the smallest cardinality of a weakly connected independent dominating set of G. Similarly, the upper weakly connected independent domination number β w (G) of G is the largest cardinality of a weakly connected independent dominating set of G. A dominating set S is called a restrained dominating set of G if for every u V (G)\S, there exists w V (G)\S such that uw E(G). The restrained domination number of G, denoted by γ r (G), is the smallest cardinality of a secure dominating set of G. A set S is called a restrained weakly connected independent dominating set of G if S is a weakly connected independent dominating set of G and for every u V (G)\S, there exists w V (G)\S such that uw E(G). The restrained weakly connected independent domination number of G, denoted by i rw (G), is the smallest cardinality of a restrained weakly connected dominating set of G. The concept of weakly connected independent domination is discussed in [3] [4], and [5]. Another domination parameter is the restrained domination which was discussed in [1], [2], and [5]. A combination of these two concepts give rise to a new variant of domination called restrained weakly connected independent domination. 2 Corona of Graphs Let G and H be graphs of order m and n, respectively. The corona G H of G and H is the graph obtained by taking one copy of G and m copies of H, and then joining the ith vertex of G to every vertex of the ith copy of H. For every v V (G), denote by H v the copy of H whose vertices are attached one by one to the vertex v. Denote by v + H v the subgraph of the corona G H corresponding to the join {v} + H v.
3 Restrained weakly connected independent domination 975 The following theorem will be useful. Theorem 2.1 Let G be a connected graph of order n 3 and let K 1 = {v}. Then S V (K 1 +G) is a restrained weakly connected independent dominating set of K 1 + G if and only if one of the following holds: (i) S = {v}. (ii) S is an independent dominating set of G. Proof : Suppose S V (K 1 + G) is a restrained weakly connected independent dominating set of K 1 +G. If v / S, then S V (G). Clearly S is a dominating set of G. For the converse, if S = {v}, then S is a restrained weakly connected independent dominating of K 1 + G. Suppose S is an independent dominating set of G. Then S is a weakly connected independent dominating set of K 1 +G. Since vx E(K 1 + G) for all x V (G)\S, it follows that S is a restrained weakly connected independent dominating set of K 1 + G. The following result characterizes the restrained weakly connected independent domination in the corona of two connected graphs. Theorem 2.2 Let G and H be connected graphs of order m 2 and n 3, respectively. Then S V (G H) is a restrained weakly connected independent dominating set of G H if and only if S = S 1, where S 1 is v V (G)\S 1 S v a weakly connected independent dominating set of G and S v is an independent dominating set of H v for all v V (G)\S 1. Proof : Suppose S V (G H) be a restrained weakly connected independent dominating set of G H. Let S 1 = S V (G). Since S is a weakly connected independent dominating set of G, S 1 is a weakly connected independent dominating set of G. Let v V (G)\S 1. By Theorem 2.1, S v is an independent dominating set of H v. Hence, S = S 1. Conversely, suppose S = S 1 v V (G)\S 1 S v v V (G)\S 1 S v, where S 1 is a weakly connected independent dominating set of G and S v is an independent dominating set of H v for all v V (G)\S 1. By Theorem 2.1, {v} is a restrained weakly connected independent dominating set of v + H v for each v S 1 and S v is a restrained weakly connected independent dominating set of v + H v for each v / S 1. Therefore, S is a restrained weakly connected independent dominating set of G H.
4 976 Rene E. Leonida The following theorem can be found in [4]. Theorem 2.3 Let G be a connected graph of order m and H any graph with i(h) 1. If C V (G H) is a minimum weakly connected independent dominating set of G H, then C V (G) is a maximum weakly connected independent dominating set of G. Corollary 2.4 Let G and H be connected graphs of order m 2 and n 3, respectively. Then i rw (G H) = β w (G) + (m β w (G))i(H). Proof : The corollary clearly holds when i(h) = 1. Suppose i(h) 1. Let S 1 be a maximum weakly connected independent dominating set of G and S be a minimum independent dominating set of H. For each v V (G)\S 1, let S v V (H v ) be such that S v = S. Let S 2 = {S v : v V (G)\S 1 }. By Theorem 2.2, S = S 1 S 2 is a restrained weakly connected independent dominating set of G H. Thus, i rw (G H) S = S 1 + v V (G)\S 1 S v = β w (G) + (m β w (G))i(H). Next, let S be a minimum restrained weakly connnected independent dominating set of G H. Let S 1 = S V (G) and S 2 = S \S 1. For each u V (G)\S 1, let S u V (H u ) be an independent dominating set of H u. Then S 2 = {S u : u V (G)\S 1 }. By Theorem 2.3, S 1 is a maximum weakly connected independent dominating set of G. Thus, S 1 = β w (G). Hence, i rw (G H) = S = S 1 + u V (G)\S 1 S u β w (G) + (m β w (G))i(H). Therefore, i rw (G H) = β w (G) + (m β w (G))i(H). 3 Composition of Graphs Observe that a subset C of V (G[H]) = V (G) V (H) can be written as C = ({x} T x ), where S V (G) and T x V (H) for every x S. Henceforth, we shall use this form to denote any subset C of V (G[H]). The following result can be found in [5]. Theorem 3.1 Let G be a nontrivial connected graph and H any graph. A subset C = ({x} T x ) of V (G[H]) is a weakly connected independent dominating set of G[H] if and only if S is a weakly connected independent dominating set of G and T x is an independent dominating set of H for every x S.
5 Restrained weakly connected independent domination 977 A similar result characterizes the restrained weakly connected independent dominating set of G[H]. Theorem 3.2 Let G and H be nontrivial connected graphs. A subset C = ({x} T x ) of V (G[H]) is a restrained weakly connected independent dominating set of G[H] if and only if S is a weakly connected independent dominating set of G and T x is an independent dominating set of H for every x S. Proof : Suppose C is a restrained weakly connected independent dominating set of G[H]. By Theorem 3.1, C = ({x} T x ), where S is a weakly connected independent dominating set of G and T x is an independent dominating set of H for every x S. Conversely, suppose C = ({x} T x ), where S is a weakly connected independent dominating set of G and T x is an independent dominating set of H for every x S. By Theorem 3.1, C is a weakly connected independent dominating set of G[H]. Now, let (u, a) V (G[H])\C. Consider the following cases: Case 1. u S. Since S is a dominating set of G, choose w V (G)\S such that uw E(G). Hence, (w, a) V (G[H])\C and (u, a)(w, a) E(G[H]). Case 2. u / S. Since H is a nontrivial connected graph, there exists b V (H)\{a} such that ab E(H). Thus, (u, b) V (G[H])\C and (u, a)(u, b) E(G[H]). Therefore, C is a restrained weakly connected independent dominating set of G[H]. Corollary 3.3 Let G and H be nontrivial connected graphs. Then i rw (G[H]) = i w (G)i(H). Proof : Let C = ({x} T x ) be a minimum restrained weakly connected independent dominating set of G[H]. By Theorem 3.2, S is a weakly connected independent dominating set of G and T x is an independent dominating set of H for every x S. Hence, i rw (G[H]) = C = ({x} T x) = S Tx i w (G)i(H). Next, let S be a minimum weakly connected independent dominating set of G and D a minimum independent dominating set of H. For each x S, let T x = D. By Theorem 3.2, C = ({x} T x ) is a restrained weakly connected independent dominating set of G[H]. Thus,
6 978 Rene E. Leonida i rw (G[H]) C = ({x} T x) = S D = iw (G)i(H). Therefore, i rw (G[H]) = i w (G)i(H). References [1] S. R. Canoy, Jr., Restrained Domination in Graphs Under Some Binary Operations, Applied Mathematical Sciences, 8(2014), [2] G. S. Domke, J. H. Hattingh, S. T. Hedetniemi, R. C. Laskar, and L. R. Marcus, Restrained Domination in Graphs, Discrete Math., 203(1999), [3] R. E. Leonida, Weakly Connected Independent Dominations in the Join of Graphs, International Math. Forum, 8(2013), [4] R. E. Leonida and S. R. Canoy, Jr., Weakly Convex and Weakly Connected Independent Dominations in the Corona of Graphs, International Mathematical Forum, 8(2013), [5] R. E. Leonida, E. P. Sandueta, and S. R. Canoy, Jr., Weakly Connected Independent and Weakly Connected Total Dominations in a Product of Graphs, Applied Mathematical Sciences, 8(2014), [6] N. Tuan and S. R. Canoy, Jr. Independent Restrained Domination in Graphs, Applied Mathematical Sciences, 8(2014), Received: January 3, 2015; Published: February 1, 2015
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 informationSecure 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 informationRestrained 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 informationLocating-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 informationSecure 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 informationOn 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 informationp-liar s Domination in a Graph
Applied Mathematical Sciences, Vol 9, 015, no 107, 5331-5341 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/ams0155749 p-liar s Domination in a Graph Carlito B Balandra 1 Department of Arts and Sciences
More informationAnother Look at p-liar s Domination in Graphs
International Journal of Mathematical Analysis Vol 10, 2016, no 5, 213-221 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ijma2016511283 Another Look at p-liar s Domination in Graphs Carlito B Balandra
More information1-movable Independent Outer-connected Domination in Graphs
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 1 (2017), pp. 41 49 Research India Publications http://www.ripublication.com/gjpam.htm 1-movable Independent Outer-connected
More information1-movable Restrained Domination in Graphs
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 6 (2016), pp. 5245-5225 Research India Publications http://www.ripublication.com/gjpam.htm 1-movable Restrained Domination
More informationInduced 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 informationThe 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 informationDouble 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 informationIndependent 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 informationSome 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 informationOn Disjoint Restrained Domination in Graphs 1
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 3 (2016), pp. 2385-2394 Research India Publications http://www.ripublication.com/gjpam.htm On Disjoint Restrained Domination
More informationMore 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 informationInverse Closed Domination in Graphs
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 2 (2016), pp. 1845-1851 Research India Publications http://www.ripublication.com/gjpam.htm Inverse Closed Domination in
More informationRainbow 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 informationA Characterization of the Cactus Graphs with Equal Domination and Connected Domination Numbers
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 7, 275-281 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.7932 A Characterization of the Cactus Graphs with
More informationDouble 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 informationOn Symmetric Bi-Multipliers of Lattice Implication Algebras
International Mathematical Forum, Vol. 13, 2018, no. 7, 343-350 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2018.8423 On Symmetric Bi-Multipliers of Lattice Implication Algebras Kyung Ho
More informationMappings 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 informationLocating 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 informationNote 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 informationDirect 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 informationAxioms of Countability in Generalized Topological Spaces
International Mathematical Forum, Vol. 8, 2013, no. 31, 1523-1530 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.37142 Axioms of Countability in Generalized Topological Spaces John Benedict
More informationEdge 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 informationRegular 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 informationRoot 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 informationContra 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 informationGraceful Labeling for Complete Bipartite Graphs
Applied Mathematical Sciences, Vol. 8, 2014, no. 103, 5099-5104 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.46488 Graceful Labeling for Complete Bipartite Graphs V. J. Kaneria Department
More informationInternational 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 informationOn Regular Prime Graphs of Solvable Groups
International Journal of Algebra, Vol. 10, 2016, no. 10, 491-495 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2016.6858 On Regular Prime Graphs of Solvable Groups Donnie Munyao Kasyoki Department
More informationSolving 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 informationDiophantine Equations. Elementary Methods
International Mathematical Forum, Vol. 12, 2017, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.7223 Diophantine Equations. Elementary Methods Rafael Jakimczuk División Matemática,
More informationIntegration over Radius-Decreasing Circles
International Journal of Mathematical Analysis Vol. 9, 2015, no. 12, 569-574 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.47206 Integration over Radius-Decreasing Circles Aniceto B.
More informationACG M and ACG H Functions
International Journal of Mathematical Analysis Vol. 8, 2014, no. 51, 2539-2545 HIKARI Ltd, www.m-hiari.com http://dx.doi.org/10.12988/ijma.2014.410302 ACG M and ACG H Functions Julius V. Benitez Department
More informationInverse and Disjoint Restrained Domination in Graphs
Intern. J. Fuzzy Mathematical Archive Vol. 11, No.1, 2016, 9-15 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 17 August 2016 www.researchmathsci.org International Journal of Inverse and Disjoint
More informationA Note of the Strong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 10, 2016, no. 6, 255-261 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.511700 A Note of the Strong Convergence of the Mann Iteration for Demicontractive
More informationApproximations 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 informationALL GRAPHS WITH PAIRED-DOMINATION NUMBER TWO LESS THAN THEIR ORDER. Włodzimierz Ulatowski
Opuscula Math. 33, no. 4 (2013), 763 783 http://dx.doi.org/10.7494/opmath.2013.33.4.763 Opuscula Mathematica ALL GRAPHS WITH PAIRED-DOMINATION NUMBER TWO LESS THAN THEIR ORDER Włodzimierz Ulatowski Communicated
More informationA Generalization of p-rings
International Journal of Algebra, Vol. 9, 2015, no. 8, 395-401 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2015.5848 A Generalization of p-rings Adil Yaqub Department of Mathematics University
More informationµs p -Sets and µs p -Functions
International Journal of Mathematical Analysis Vol. 9, 2015, no. 11, 499-508 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.412401 µs p -Sets and µs p -Functions Philip Lester Pillo
More informationFuzzy 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 informationDevaney'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 informationA note on the total domination number of a tree
A note on the total domination number of a tree 1 Mustapha Chellali and 2 Teresa W. Haynes 1 Department of Mathematics, University of Blida. B.P. 270, Blida, Algeria. E-mail: m_chellali@yahoo.com 2 Department
More informationRegular Weakly Star Closed Sets in Generalized Topological Spaces 1
Applied Mathematical Sciences, Vol. 9, 2015, no. 79, 3917-3929 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.53237 Regular Weakly Star Closed Sets in Generalized Topological Spaces 1
More informationIntroduction to Domination Polynomial of a Graph
Introduction to Domination Polynomial of a Graph arxiv:0905.2251v1 [math.co] 14 May 2009 Saeid Alikhani a,b,1 and Yee-hock Peng b,c a Department of Mathematics Yazd University 89195-741, Yazd, Iran b Institute
More informationOrder-theoretical Characterizations of Countably Approximating Posets 1
Int. J. Contemp. Math. Sciences, Vol. 9, 2014, no. 9, 447-454 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2014.4658 Order-theoretical Characterizations of Countably Approximating Posets
More information2-bondage in graphs. Marcin Krzywkowski*
International Journal of Computer Mathematics Vol. 00, No. 00, January 2012, 1 8 2-bondage in graphs Marcin Krzywkowski* e-mail: marcin.krzywkowski@gmail.com Department of Algorithms and System Modelling
More informationCaristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces
International Journal of Mathematical Analysis Vol. 11, 2017, no. 6, 267-275 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.717 Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric
More informationOn the Probability that a Group Element Fixes a Set and its Generalized Conjugacy Class Graph
International Journal of Mathematical Analysis Vol. 9, 2015, no. 4, 161-167 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.411336 On the Probability that a roup Element Fixes a Set and
More informationGeometric Properties of Square Lattice
Applied Mathematical Sciences, Vol. 8, 014, no. 91, 4541-4546 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.014.46466 Geometric Properties of Square Lattice Ronalyn T. Langam College of Engineering
More informationGeneralized Derivation on TM Algebras
International Journal of Algebra, Vol. 7, 2013, no. 6, 251-258 HIKARI Ltd, www.m-hikari.com Generalized Derivation on TM Algebras T. Ganeshkumar Department of Mathematics M.S.S. Wakf Board College Madurai-625020,
More informationPrime and Semiprime Bi-ideals in Ordered Semigroups
International Journal of Algebra, Vol. 7, 2013, no. 17, 839-845 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2013.310105 Prime and Semiprime Bi-ideals in Ordered Semigroups R. Saritha Department
More informationComplete Ideal and n-ideal of B-algebra
Applied Mathematical Sciences, Vol. 11, 2017, no. 35, 1705-1713 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.75159 Complete Ideal and n-ideal of B-algebra Habeeb Kareem Abdullah University
More informationOn 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 informationInternational Journal of Algebra, Vol. 7, 2013, no. 3, HIKARI Ltd, On KUS-Algebras. and Areej T.
International Journal of Algebra, Vol. 7, 2013, no. 3, 131-144 HIKARI Ltd, www.m-hikari.com On KUS-Algebras Samy M. Mostafa a, Mokhtar A. Abdel Naby a, Fayza Abdel Halim b and Areej T. Hameed b a Department
More informationOn 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 informationOn Uniform Limit Theorem and Completion of Probabilistic Metric Space
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 10, 455-461 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4120 On Uniform Limit Theorem and Completion of Probabilistic Metric Space
More informationDiameter 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 informationLocating-Total Dominating Sets in Twin-Free Graphs: a Conjecture
Locating-Total Dominating Sets in Twin-Free Graphs: a Conjecture Florent Foucaud Michael A. Henning Department of Pure and Applied Mathematics University of Johannesburg Auckland Park, 2006, South Africa
More informationβ 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 informationOn 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 informationSome New Approaches for Computation of Domination Polynomial of Specific Graphs
Journal of Mathematical Extension Vol. 8, No. 2, (2014), 1-9 Some New Approaches for Computation of Domination Polynomial of Specific Graphs S. Alikhani Yazd University E. Mahmoudi Yazd University M. R.
More informationThe Split Hierarchical Monotone Variational Inclusions Problems and Fixed Point Problems for Nonexpansive Semigroup
International Mathematical Forum, Vol. 11, 2016, no. 8, 395-408 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2016.6220 The Split Hierarchical Monotone Variational Inclusions Problems and
More informationOn Annihilator Small Intersection Graph
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 7, 283-289 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.7931 On Annihilator Small Intersection Graph Mehdi
More informationRemarks on Fuglede-Putnam Theorem for Normal Operators Modulo the Hilbert-Schmidt Class
International Mathematical Forum, Vol. 9, 2014, no. 29, 1389-1396 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.47141 Remarks on Fuglede-Putnam Theorem for Normal Operators Modulo the
More informationGeneralized Boolean and Boolean-Like Rings
International Journal of Algebra, Vol. 7, 2013, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2013.2894 Generalized Boolean and Boolean-Like Rings Hazar Abu Khuzam Department
More informationH 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 informationInner Variation and the SLi-Functions
International Journal of Mathematical Analysis Vol. 9, 2015, no. 3, 141-150 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.411343 Inner Variation and the SLi-Functions Julius V. Benitez
More informationStrong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 9, 015, no. 4, 061-068 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.5166 Strong Convergence of the Mann Iteration for Demicontractive Mappings Ştefan
More informationWeak Resolvable Spaces and. Decomposition of Continuity
Pure Mathematical Sciences, Vol. 6, 2017, no. 1, 19-28 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/pms.2017.61020 Weak Resolvable Spaces and Decomposition of Continuity Mustafa H. Hadi University
More informationDomination and Total Domination Contraction Numbers of Graphs
Domination and Total Domination Contraction Numbers of Graphs Jia Huang Jun-Ming Xu Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, China Abstract In this
More informationSupra g-closed Sets in Supra Bitopological Spaces
International Mathematical Forum, Vol. 3, 08, no. 4, 75-8 HIKARI Ltd, www.m-hikari.com https://doi.org/0.988/imf.08.8 Supra g-closed Sets in Supra Bitopological Spaces R. Gowri Department of Mathematics
More informationINDEPENDENT TRANSVERSAL DOMINATION IN GRAPHS
Discussiones Mathematicae Graph Theory 32 (2012) 5 17 INDEPENDENT TRANSVERSAL DOMINATION IN GRAPHS Ismail Sahul Hamid Department of Mathematics The Madura College Madurai, India e-mail: sahulmat@yahoo.co.in
More information-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 informationConvex Sets Strict Separation in Hilbert Spaces
Applied Mathematical Sciences, Vol. 8, 2014, no. 64, 3155-3160 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.44257 Convex Sets Strict Separation in Hilbert Spaces M. A. M. Ferreira 1
More informationKKM-Type Theorems for Best Proximal Points in Normed Linear Space
International Journal of Mathematical Analysis Vol. 12, 2018, no. 12, 603-609 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2018.81069 KKM-Type Theorems for Best Proximal Points in Normed
More informationRelations between edge removing and edge subdivision concerning domination number of a graph
arxiv:1409.7508v1 [math.co] 26 Sep 2014 Relations between edge removing and edge subdivision concerning domination number of a graph Magdalena Lemańska 1, Joaquín Tey 2, Rita Zuazua 3 1 Gdansk University
More informationA Generalization of Generalized Triangular Fuzzy Sets
International Journal of Mathematical Analysis Vol, 207, no 9, 433-443 HIKARI Ltd, wwwm-hikaricom https://doiorg/02988/ijma2077350 A Generalization of Generalized Triangular Fuzzy Sets Chang Il Kim Department
More informationDomination in Cayley Digraphs of Right and Left Groups
Communications in Mathematics and Applications Vol. 8, No. 3, pp. 271 287, 2017 ISSN 0975-8607 (online); 0976-5905 (print) Published by RGN Publications http://www.rgnpublications.com Domination in Cayley
More informationA Novel Approach: Soft Groups
International Journal of lgebra, Vol 9, 2015, no 2, 79-83 HIKRI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ija2015412121 Novel pproach: Soft Groups K Moinuddin Faculty of Mathematics, Maulana zad National
More informationFormula for Lucas Like Sequence of Fourth Step and Fifth Step
International Mathematical Forum, Vol. 12, 2017, no., 10-110 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.612169 Formula for Lucas Like Sequence of Fourth Step and Fifth Step Rena Parindeni
More informationDouble domination edge removal critical graphs
AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 48 (2010), Pages 285 299 Double domination edge removal critical graphs Soufiane Khelifi Laboratoire LMP2M, Bloc des laboratoires Université demédéa Quartier
More informationDecompositions 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 informationA Short Note on Universality of Some Quadratic Forms
International Mathematical Forum, Vol. 8, 2013, no. 12, 591-595 HIKARI Ltd, www.m-hikari.com A Short Note on Universality of Some Quadratic Forms Cherng-tiao Perng Department of Mathematics Norfolk State
More informationOn a Boundary-Value Problem for Third Order Operator-Differential Equations on a Finite Interval
Applied Mathematical Sciences, Vol. 1, 216, no. 11, 543-548 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.216.512743 On a Boundary-Value Problem for Third Order Operator-Differential Equations
More informationAnalogies and discrepancies between the vertex cover number and the weakly connected domination number of a graph
Analogies and discrepancies between the vertex cover number and the weakly connected domination number of a graph M. Lemańska a, J. A. Rodríguez-Velázquez b, Rolando Trujillo-Rasua c, a Department of Technical
More informationBounded Subsets of the Zygmund F -Algebra
International Journal of Mathematical Analysis Vol. 12, 2018, no. 9, 425-431 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2018.8752 Bounded Subsets of the Zygmund F -Algebra Yasuo Iida Department
More informationON THE NUMBERS OF CUT-VERTICES AND END-BLOCKS IN 4-REGULAR GRAPHS
Discussiones Mathematicae Graph Theory 34 (2014) 127 136 doi:10.7151/dmgt.1724 ON THE NUMBERS OF CUT-VERTICES AND END-BLOCKS IN 4-REGULAR GRAPHS Dingguo Wang 2,3 and Erfang Shan 1,2 1 School of Management,
More informationConvex Sets Strict Separation. in the Minimax Theorem
Applied Mathematical Sciences, Vol. 8, 2014, no. 36, 1781-1787 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.4271 Convex Sets Strict Separation in the Minimax Theorem M. A. M. Ferreira
More informationOn Positive Stable Realization for Continuous Linear Singular Systems
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 8, 395-400 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4246 On Positive Stable Realization for Continuous Linear Singular Systems
More informationAlgebraic Models in Different Fields
Applied Mathematical Sciences, Vol. 8, 2014, no. 167, 8345-8351 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.411922 Algebraic Models in Different Fields Gaetana Restuccia University
More informationA Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating Polynomials
Applied Mathematical Sciences, Vol. 8, 2014, no. 35, 1723-1730 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.4127 A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating
More informationToric Deformation of the Hankel Variety
Applied Mathematical Sciences, Vol. 10, 2016, no. 59, 2921-2925 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.6248 Toric Deformation of the Hankel Variety Adelina Fabiano DIATIC - Department
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationOn Domination Critical Graphs with Cutvertices having Connected Domination Number 3
International Mathematical Forum, 2, 2007, no. 61, 3041-3052 On Domination Critical Graphs with Cutvertices having Connected Domination Number 3 Nawarat Ananchuen 1 Department of Mathematics, Faculty of
More informationA Bound on Weak Domination Number Using Strong (Weak) Degree Concepts in Graphs
ISSN 974-9373 Vol. 5 No.3 (2) Journal of International Academy of Physical Sciences pp. 33-37 A Bound on Weak Domination Number Using Strong (Weak) Degree Concepts in Graphs R. S. Bhat Manipal Institute
More information