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

More documents

Recommendations

Info

138 BIBLIOGRAPHY[46] P. Erdös, and A. Rényi, On a Problem in the Theory of Graphs, Publ.Math.Inst.Hungar.Acad.Sci. 7 (1962), 623 - 641.[47] M. Essalih, M. El Marraki, and G.Alhagri, Calculation of some topologicalindices of graphs, Journal of Theoretical and Applied Information Technology(JATIT), Vol. 30 No.2 (2011), 122 - 127.[48] M. Fiedler, Algebraic Connectivity of Graphs, Czechoslovak Mathematical Journal,23 (1973), 298 - 305.[49] W. Feussner, Zur Berechnung der Stromsträrke in netzförmigen Letern, Ann.Phys., 15 (1904), 385 - 394.[50] B. Gilbert, W. Myrvold, Maximizing spanning trees in almost complete graphs,Networks 30 (1997), 97 - 104.[51] I. P. Goulden and D.M. Jackson, Combinatorial Enumeration, John Wiley &Sons Inc., New York, 1983.[52] R. Grone and R. Merris, The Laplacian Spectrum of a Graph II, SIAM Journalon discrete Mathematics 7 (1994) 221 - 229.[53] R. Grone, R. Merris and V. S. Sunder, The Laplacian Spectrum of a Graph,SIAM Journal on Matrix Analysis and its Applications 11 (1990) 218 - 238.[54] I. Gutman, Y. N. Yeh, S. L. Lee and J. C. Chen, Wiener numbers of dendrimers,MATCH (Commun. Math. Comput. Chem) 30 (1994), pp. 103 - 115.[55] P. L. Hammer, A. K. Kel’mans, Laplacian Spectra and Spanning Trees of ThresholdGraphs, Discrete Applied Mathematics 65 (1996) 255 - 273.[56] F. Harary, Graph theory, Addison-Wesley, Reading, MA, 1969.[57] J. M. Harris, J. L. Hirst, and M. J. Mossinghoff, Combinatorics and GraphTheory, Springer, 2008.[58] S. Janson, The Wiener index of simply generated random trees, Random Struct.Alg. 22 (2003), no. 4, 337 - 358.[59] S. Janson, T. Luczak and A. Ruciński, Random Graphs, Wiley and Sons, NewYork 2000.[60] A. K. Kel’mans, Comparison of graphs by their number of spanning trees, DiscreteMathematics, 16 (3) (1976), 241 - 261.[61] A. K. Kel’mans, Spanning trees of extended graphs, Combinatorica, 12 (1) (1992),45 - 51.
BIBLIOGRAPHY 139[62] A. K. Kel’mans, The number of trees in a graph I, Automat. Remote Control, 26(1965), 2118 - 2129.[63] A. K. Kel’mans, The number of trees in a graph II, Automat. Remote Control, 27(1966), 233 - 241.[64] A. K. Kel’mans, V. M. Chelnokov, A certain polynomial of a graph and graphswith an extremal number of trees, J. Comb. Theory, (B) 16 (1974), 197 - 214.[65] G. G. Kirchhoff, Über die Auflösung der Gleichungen, auf welche man bei derUntersuchung der linearen Verteilung galvanischer Strme gefhrt wird , Ann. Phys.Chem., 72, (1847) 497 - 508.[66] D. J. Kleitman, B. Golden, Counting Trees in a Certain Class of Graphs, Amer.Math. Monthly, 82 (1975), 40 - 44.[67] D. E. Knuth, Aztec Diamonds, Checkerboard Graphs, and Spanning trees, J. Alg.Combinatorics 6 (1997), 253 - 257.[68] A. V. Kostochka, The number spanning trees in graphs with a given degree sequence,Random Structures and Algorithms, 6 (1995), no. 2-3, 269 - 274.[69] S.K. Lando and A. Zvonkin, Graphs on Surfaces and Their Applications.Springer-Verlag, 2004.[70] S.K. Lando and A. Zvonkin, Meanders. Selecta Mathematica Sovietica, vol. 11(1992), no. 2, 117 - 144.[71] László Lovász, József Pelikán, and Katalin Vesztergombi, Discrete mathematics,Elementary and beyond, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 2003.[72] R. P. Lewis, The number of spanning trees of a complete multipartite graph, DiscreteMathematics, 197/198 (1999), 537 - 541.[73] X. L. Li and F. J. Zhang, On the numbers of spanning trees and Eulerian toursin generalized de Bruijn graphs, Discrete Mathematics, 94 (1997), 189 - 197.[74] Z. Lonc, K. Parol, J. M. Wojciechowski, On the asymptotic behavior of themaximum number of spanning trees in circulant graphs, Networks, 30 (1) (1997), 47- 56.[75] Z. Lonc, K. Parol, J. M. Wojciechowski, On the numbers of spanning trees indirected circulant graphs, Networks, 73 (3) (2001), 129 - 133.[76] D. Lotfi, M. El Marraki and A. Modabish, Recursive relation for counting thecomplexity of butterfly map. Journal of Theoretical and Applied Information Technology(JATIT), Vol. 29, 2011, no. 1, 43 - 46.
Page 3:
1To my daughter Hanin.
Page 6 and 7:
4my wife who has been very supporti
Page 8 and 9:
6 CONTENTSII Theoretical Part 533 H
Page 10 and 11:
8 CONTENTS
Page 14 and 15:
12 LIST OF FIGURES7.11 The maps F n
Page 16:
14 LIST OF TABLES
Page 19 and 20:
LIST OF TABLES 17the n-Barrel chain
Page 21:
Part IPreliminaries19
Page 24 and 25:
22 CHAPTER 1. DEFINITIONS AND PROPE
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
42 CHAPTER 2. SPANNING TREESFigure
Page 46 and 47:
44 CHAPTER 2. SPANNING TREESThe num
Page 48 and 49:
46 CHAPTER 2. SPANNING TREESExample
Page 50 and 51:
48 CHAPTER 2. SPANNING TREESFor exa
Page 52 and 53:
50 CHAPTER 2. SPANNING TREESIn the
Page 54 and 55:
52 CHAPTER 2. SPANNING TREES
Page 57 and 58:
Chapter 3How to count the number of
Page 59 and 60:
3.3. Counting the number of spannin
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Chapter 4New methods to compute the
Page 71 and 72:
4.3. Main Results 69one vertex (any
Page 73 and 74:
4.3. Main Results 71Lemma 4.3.8 Let
Page 75 and 76:
4.3. Main Results 73This recursion
Page 77 and 78:
4.3. Main Results 75Proof: It is th
Page 79 and 80:
4.3. Main Results 77Figure 4.12: An
Page 81 and 82:
4.3. Main Results 79Theorem 4.3.31
Page 83 and 84:
4.3. Main Results 81Property 4.3.33
Page 85:
Part IIIUse of Derived Theoretical
Page 88 and 89:
CHAPTER 5.86THE NUMBER OF SPANNING
Page 90 and 91: CHAPTER 5.88THE NUMBER OF SPANNING
Page 110 and 111: CHAPTER 6.108COUNTING THE NUMBER OF
Page 118 and 119: 116 CHAPTER 7. MAXIMAL PLANAR MAPSF
Page 122 and 123: 120 CHAPTER 7. MAXIMAL PLANAR MAPSR
Page 124 and 125: 122 CHAPTER 7. MAXIMAL PLANAR MAPSP
Page 126 and 127: 124 CHAPTER 7. MAXIMAL PLANAR MAPS7
Page 128 and 129: 126 CHAPTER 7. MAXIMAL PLANAR MAPSa
Page 130 and 131: 128 CHAPTER 7. MAXIMAL PLANAR MAPST
Page 132 and 133: 130 CHAPTER 7. MAXIMAL PLANAR MAPSP
Page 136 and 137: 134 CHAPTER 7. MAXIMAL PLANAR MAPSI
Page 138 and 139: 136 BIBLIOGRAPHY[13] N. Biggs, E. L
Page 142 and 143: 140 BIBLIOGRAPHY[77] D. Lotfi, M. E
Page 144 and 145: 142 BIBLIOGRAPHY[107] R. Shrock and
Page 146 and 147: Auteur :Titre :Directeurs de thèse
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?