enumeration of the number of spanning trees in some ... - Toubkal

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142 BIBLIOGRAPHY[107] R. Shrock and F. Y. Wu, Spanning Trees on graphs and lattices in d dimensions,J. Phys A33 (2000), 3881 - 3902.[108] R. P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press,Cambridge, 1997.[109] R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press,London, 1999.[110] R. P. Stanley, Spanning trees of Aztec diamond, Discrete Mathematics, 157(1996), 375 - 388.[111] H. Temperley, On the mutual cancellation of cluster integrals in Mayer’s fugacityseries, Proc. Phys. Soc. Lond., (A) 83 (1964), 3 - 16.[112] C. Thomassen, Spanning trees and orientations of graphs, Journal of Combinatorics,Vol. 1, no. 2, pp. 101 - 111, 2010.[113] J. H. van Lint, R. M. Wilson, A course in Combinatorics, Cambridge UniversityPress, London, 1992.[114] D. G. Wagner, Combinatorics of electrical networks, Lecture notes, 2009.[115] H. Wang, The extremal values of the Wiener index of a tree with given degreeSequence, Discrete Applied Mathematics, 156 (2009) 2647 - 2654.[116] L. Weinberg, Number of Trees in a Graph, Proc. IRE, 46 (1958), 1945 - 1955.[117] D. B. West, Introduction to Graph Theory. Second Edition, Prentice Hall, 2002.[118] R. J. Wilson, Introduction to Graph Theory, 4th ed., Longman, 1996.[119] D. K. Wind and H. W. Vildhøj, Supplementary Notes for Graph Theory I.DRAFT Compiled, jun 2011.[120] F. Y. Wu, Number of spanning trees on a lattice, J. Physics, A: Mathematical andGeneral 10 (1977), L113 - 115.[121] J. Xu, Theory and Application of Graphs, Kluwer Academic Publishers, Dordrecht/Boston/London,2003.[122] W. M. Yan, W. Myrvold, K. L. Chung, A formula for the number of spanningtrees of a multi-star related graph, Information Processing Letters, 68 (1998), 295 -298.[123] X. Yong, Talip, Acenjian, The Number of Spanning trees of the Cubic CycleCN 3 and the Quadruple Cycle C4 N , Discrete Mathematics, 169 (1997), 293 - 298.
BIBLIOGRAPHY 143[124] X. Yong, F. J. Zhang, A Simple Proof for the Complexity of Square Cycle C 2 p,J. Xinjiang Univ., 11 (1994), 12 - 16.[125] X. D. Zhang, The Wiener index of trees with given degree sequences, MATCHCommun. Math. Comput. Chem., 60 (2008) 623 - 644.[126] F.J. Zhang, X.R. Yong, Asymptotic enumeration theorems for the numbers ofspanning trees and Eulerian trails in circulant digraphs & graphs, Sci. China, Ser. A43 (2) (1999) 264 - 271.[127] Y. P. Zhang, X. Yong, M. J. Golin, The number of spanning trees in circulantgraphs, Discrete Mathematics, 223 (2000), 337 - 350.[128] H. X. Zhang, F. J. Zhang and Q. X. Huang, On the number of spanning treesand Eulerian tours in iterated line graphs, Discrete Appl. Math., 73 (1997), 59 - 67.
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1To my daughter Hanin.
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4my wife who has been very supporti
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6 CONTENTSII Theoretical Part 533 H
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8 CONTENTS
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12 LIST OF FIGURES7.11 The maps F n
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14 LIST OF TABLES
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LIST OF TABLES 17the n-Barrel chain
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Part IPreliminaries19
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22 CHAPTER 1. DEFINITIONS AND PROPE
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42 CHAPTER 2. SPANNING TREESFigure
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44 CHAPTER 2. SPANNING TREESThe num
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46 CHAPTER 2. SPANNING TREESExample
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48 CHAPTER 2. SPANNING TREESFor exa
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50 CHAPTER 2. SPANNING TREESIn the
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52 CHAPTER 2. SPANNING TREES
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Chapter 3How to count the number of
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3.3. Counting the number of spannin
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Chapter 4New methods to compute the
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4.3. Main Results 69one vertex (any
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4.3. Main Results 71Lemma 4.3.8 Let
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4.3. Main Results 73This recursion
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4.3. Main Results 75Proof: It is th
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4.3. Main Results 77Figure 4.12: An
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4.3. Main Results 79Theorem 4.3.31
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4.3. Main Results 81Property 4.3.33
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Part IIIUse of Derived Theoretical
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CHAPTER 5.86THE NUMBER OF SPANNING
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Page 94 and 95: CHAPTER 5.92THE NUMBER OF SPANNING
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Page 138 and 139: 136 BIBLIOGRAPHY[13] N. Biggs, E. L
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