Bibliography. [1] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer Graduate Texts in Mathematics

Size: px

Start display at page:

Download "Bibliography. [1] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer Graduate Texts in Mathematics"

Todd Riley
5 years ago
Views:

1 Bibliography [1] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer Graduate Texts in Mathematics 244, (2008). [2] B. Bollobas, Modern Graph Theory, Springer Graduate Texts in Mathematics 184, (1998). [3] R. Diestel, Graph Theory, Springer Graduate Texts in Mathematics 173, (2000). A vailable free at [4] D.B. West, Introduction to Graph Theory, 2nd Edition, Prentice Hall, (2000). [5] P.J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, (1996). [6] J.H. van Lint and R.M. Wilson, A Course in Combinatorics, Cambridge University Press, (1992). [7] R. Stanley, Enumerative Combinatorics, Vol. I and Vol. II, Cambridge University Press, (2000/2001). [8] R. Bhatia, Matrix Analysis, Springer Graduate Texts in Mathematics 169, (1996). [9] L. Lovlisz, Combinatorial Problems and Exercises, AMS Chelsea Publishing, 2nd Edition, (2007). [10] A. Herzberg and M.R. Murty, Sudoku Puzzles and Chromatic Polynomials, Notices of the Amer. Math. Society, 54(2007), no. 6, [11] R. Bhatia, Perturbation Bounds for Matrix Eigenvalues, SIAM Classics in Applied Mathematics, (2007). [12] C. Godsil and G. Royle, Algebraic Graph Theory, Springer Graduate Texts in Mathematics 207, (2001). [13] F.R.K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, (1997). [14] S. Hoory, N. Linial and A. Wigderson, Expander Graphs and their Applications, Bulletin of the AMS, Volume 43, Number 4, (2006), 43956l. [15] N. Alon and J. Spencer, The Probabilistic Method, Wiley-Interscience, 2nd Edition, (2000). [16] M.R. Murty, Ramanujan Graphs, Journal of the Ramanujan Math. Society, 18, No.1, (2003), [17] S.M. Cioabii and M.R. Murty, Expander Graphs and Gaps between Primes, Forum Mathematicum, Volume 20, Issue 4, (2008),

2 Index adjacency matrix, 33 Amitsur,39 Appel,3 Aryabhata, 5 Bell, 20 Bell number, 20, 27 Berge, 95 Bernoulli number, 32 Bernoulli, Jakob, 32 Bhaskara, 12 bijective function, 10 binary code, 113 Binet, 17 binomial coefficient, 11 binomial theorem, 12 Birkhoff, 90 Bose, 89 bridge, 44 Brooks, 62 Bruck,107 Bruhat order, 53 Burnside, 76 Catalan, 17 Catalan number, 17 Cauchy, 76 Cayley, 4, 42, 121 center, 51, 74 centralizer, 74 characteristic polynomial, 34 characteristic vector, 10 Chowla, 107 chromatic number, 4, 61 chromatic polynomial, 61 circuit, 1, 5 Eulerian, 9 circulant graph, 159 matrix, 158 class equation, 73 classical adjoint, 45 code, 113 codeword, 113 complement, 158 complete graph conjecture, 125 component odd, 94 contraction, 44 cost, 47 critical, 65 cut edge, 44 cycle, 3, 5 cycle index, 78 De Moivre, 13 De Morgan, 3, 121 decomposition, 130 degree, 2 even, 2 odd, 2 derangement, 25 derangements, 13 diameter, 38, 142 digraph, 7, 8 Dilworth, 136 direct product poset, 53 distance, 5 dodecahedron, 131 doubly stochastic,

3 INDEX 171 eccentricity, 39, 51 edge, 1, 2 edge chromatic number, 127 edge-boundary, 154 edge-connectivity, 95 edge-expansion, 154 Egervary, 91 eigenvalue, 34 eigenvector, 34 embedded graph, 118 endpoints, 2 Erdos, 136, 138 error-correcting code, 114 Euler, 1, 17, 18, 39, 89, 130 euler, 118 Euler, Leonhard, 6 Eulerian, 6 expander, 154 exponential generating function, 20 face, 118 factor, 130 Fermat, 137 fiber, 27 Fibonacci, 16 Fibonacci number, 16 forest, 41 formal power series, 18 four colour theorem, 3 Frobenius, 76 generalized commutator, 39 generating function, 19 genus, 123 graph, 1, 2 k-connected, 96 k-edge-connected, 96 acyclic, 41 bipartite, 3, 36, 37 complete, 3 connected, 5, 95 directed, 7, 8 disconnected, 95 finite, 2 simple, 2 weighted, 47 greatest common divisor, 30 greedy, 62 greedy algorithm, 47 group automorphism, 85 group action, 72 Gupta, 127 Guthrie, 3, 121 Haken, 3 Hall, Philip, 86 Hamilton, 3 Hamiltonian cycle, 130 Hamming distance, 113 Hasse diagram, 52 head,8 Heawood, 4, 121 Hierholzer, Karl, 6 Hungarian algorithm, 91 incidence algebra, 53 incidence matrix, 33, 105 inclusion-exclusion, 43 indegree, 8 independent path, 96 independent set, 3 induction, 4 injective function, 10 inverse, 10 invertible, 10 involution, 15, 32 isomorphic poset, 55 isomorphism, 34 job assignment, 4 Konig, 7, 91, 129 Konigsberg, 1 Kempe, 4, 121 Kirchhoff, 44 Kneser graph, 71 knight tour, 131 Kruskal,47 Kuratowski, 120 ladder Mobius, 159 Lagrange, 76 Laplacian, 40, 44 Latin rectangle, 88 Latin square, 88

4 172 INDEX lattice, 54 leaf, 41 line graph, 40 linear code, 113 linear recurrence relation, 16 loop, 2 Mobius, 123 Mobius function, 53 marriage theorem, 86 matching, 86 perfect, 86 matrix-tree theorem, 44 minimal polynomial, 37 multiple edge, 2 neighbour, 2 network,4 Newton, 12 normalizer, 75 odd girth, 40 orbit, 73 Orbit-Stabilizer formula, 73 Ore, 131 orientation, 40 orthogonal Latin square, 89 outdegree, 8 outer face, 118 P61ya,78 Paley, 158 Parker, 89 Pascal, 12 path, 5, 85 permutation, 10 parity, 11 signature, 11 permutation matrix, 34, 90 Petersen graph, 120 pigeonhole principle, 134 Pingala, 12 planar graph, 118 proper, 87 proper colouring, 59 radius, 39 Ramsey, 134 ramsey, 137 Ramsey number, 136 rank, 35 Rayleigh-Ritz quotient, 64 reduction, 53 Ringel, 125 routing, 4 Ryser, 107 scheduling, 4, 60 Schur, 137 Segner, 17, 18 Shrikhande, 89 spanning subgraph, 44 spanning tree, 44 minimum, 47 stabilizer, 73 stable set, 3 Stirling, 12 Stirling formula, 19 Stirling number of the first kind, 26 Stirling number of the second kind, 27 Stirling's formula, 13 strongly regular, 158 subgraph, 65 surjective function, 10, 25 Sylow subgroup, 75 symmetric design, 107 symmetric group, 10 system of common representatives, 89 system of distinct representatives, 88 Szekeres, 66 tail, 8 Tarry, 89 thirty-six officers, 89 torus, 123 tournament, 133 trail, 5 Eulerian, 9 transposition, 11 transversal, 91 traveling salesman problem, 130 tree, 41 Tutte,94 valence, 1, 2 vertex, 1,2 vertex-connectivity, 95 Vizing, 127

5 INDEX 173 Von Neumann, 90 walk,5 even, 5 length, 5 odd, 5 weight, 4, 113 weighted cover, 91 Wiener index, 50 Wilf, Herbert, 66 Youngs, 125 zeta function, 53

6 Texts and Readings in Mathematics 1. R. B. Bapat: Linear Algebra and Linear Models (Second Edition) 2. Rajendra Bhatia: Fourier Series (Second Edition) 3. C. Musili: Representations of Finite Groups 4. H. Helson: Linear Algebra (Second Edition) 5. D. Sarason: Complex Function Theory (Second Edition) 6. M. G. Nadkarni: Basic Ergodic Theory (Second Edition) 7. H. Helson: Harmonic Analysis (Second Edition) 8. K. Chandrasekharan: A Course on Integration Theory 9. K. Chandrasekharan: A Course on Topological Groups 10. R. Bhatia (ed.): Analysis, Geometry and Probability 11. K. R. Davidson: C* - Algebras by Example 12. M. Bhattacharjee et al.: Notes on Infinite Permutation Groups 13. V. S. Sunder: Functional Analysis - Spectral Theory 14. V. S. Varadarajan: Algebra in Ancient and Modern Times 15. M. G. Nadkarni: Spectral Theory of Dynamical Systems 16. A. Borel: Semisimple Groups and Riemannian Symmetric Spaces 17. M. Marcolli: Seiberg - Witten Gauge Theory 18. A. Bottcher and S. M. Grudsky: Toeplitz Matrices, Asymptotic Linear Algebra and Functional Analysis 19. A. R. Rao and P. Bhimasankaram: Linear Algebra (Second Edition) 20. C. Musili: Algebraic Geometry for Beginners 21. A. R. Rajwade: Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem 22. S. Kumaresan: A Course in Differential Geometry and Lie Groups 23. Stef Tijs: Introduction to Game Theory 24. B. Sury: The Congruence Subgroup Problem 25. R. Bhatia (ed.): Connected at Infinity 26. K. Mukherjea: Differential Calculus in Normed Linear Spaces (Second Edition) 27. Satya Deo: Algebraic Topology: A Primer (Corrected Reprint) 28. S. Kesavan: Nonlinear Functional Analysis: A First Course 29. S. Szab6: Topics in Factorization of Abelian Groups 30. S. Kumaresan and G. Santhanam: An Expedition to Geometry 31. D. Mumford: Lectures on Curves on an Algebraic Surface (Reprint) 32. J. W. Milnor and J. D. Stasheff: Characteristic Classes (Reprint) 33. K. R. Parthasarathy: Introduction to Probability and Measure (Corrected Reprint) 34. A. Mukherjee: Topics in Differential Topology 35. K. R. Parthasarathy: Mathematical Foundations of Quantum Mechanics 36. K. B. Athreya and S. N. Lahiri: Measure Theory 37. Terence Tao: Analysis I (Second Edition) 38. Terence Tao: Analysis II (Second Edition)

7 39. W. Decker and C. Lossen: Computing in Algebraic Geometry 40. A. Goswami and B. V. Rao: A Course in Applied Stochastic Processes 41. K. B. Athreya and S. N. Lahiri: Probability Theory 42. A. R. Rajwade and A. K. Bhandari: Surprises and Counterexamples in Real Function Theory 43. G. H. Golub and C. F. Van Loan: Matrix Computations (Reprint of the Third Edition) 44. Rajendra Bhatia: Positive Definite Matrices 45. K. R. Parthasarathy: Coding Theorems of Classical and Quantum Information Theory 46. C. S. Seshadri: Introduction to the Theory of Standard Monomials 47. Alain Connes and Matilde Marcolli: Noncommutative Geometry, Quantum Fields and Motives 48. Vivek S. Borkar: Stochastic Approximation: A Dynamical Systems Viewpoint 49. B. J. Venkatachala: Inequalities: An Approach Through Problems 50. Rajendra Bhatia: Notes on Functional Analysis 51. A. Clebsch (ed.): Jacobi's Lectures on Dynamics (Second Revised Edition) 52. S. Kesavan: Functional Analysis 53. V. Lakshmibai and Justin Brown: Flag Varieties: An Interplay of Geometry, Combinatorics, and Representation Theory 54. S. Ramasubramanian : Lectures on Insurance Models

Index. <p,2. 7r-system, 2 3,86 9\,86

$Index. <p,2. 7r-system, 2 3,86 9\,86$ Index 3,86 9\,86 (M, d), m, 12 BMP,345 Bd,105 BdJ,142 CLT,283 CF, 8;,34 Cr, Cr,514 E*, E*,3 FCLT,336 FLIL,370 LIL,367 MC,458 Rk Euclidean k-space, 2 Rk,!Jlk, C, Cff, 11 SBMP,427 SLLN,274 Ll~, 22 {:},6