Fibonacci Numbers of Generalized Zykov Sums

被引：0

作者：

Bautista-Ramos, Cesar ^{[1
]}

Guillen-Galvan, Carlos ^{[1
]}

机构：

[1] Univ Autonoma Puebla, Fac Ciencias Computac Benemerita, 14 Sur & Av San Claudio,Edif 104C 303, Puebla 72570, Pue, Mexico

来源：

JOURNAL OF INTEGER SEQUENCES | 2012年 / 15卷 / 07期

关键词：

Fibonacci number; Merrifield-Simmons index; independent set; Zykov sum; transfer matrix method;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that counting independent sets in several families of graphs can be done within the framework of generalized Zykov sums by using the transfer matrix method. Then we calculated the generating functions of the number of independent sets for families of generalized Zykov sums. We include many interesting particular cases (petersen graphs, generalized Mobius ladders, carbon nanotube graphs, among others).

引用

页数：22

共 19 条

[1] Burstein A., 2008, PURE MATH APPL, V19, P17
[2] The number of independent sets in a grid graph
Calkin, NJ
Wilf, HS
[J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 1998, 11 (01) : 54 - 60
[3] Matchings and independent sets of a fixed size in regular graphs
Carroll, Teena
Galvin, David
Tetali, Prasad
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2009, 116 (07) : 1219 - 1227
[4] Extremal Graphs for Homomorphisms
Cutler, Jonathan
Radcliffe, A. J.
[J]. JOURNAL OF GRAPH THEORY, 2011, 67 (04) : 261 - 284
[5] Diestel R., 2006, GRAPH THEORY
[6] ENGEL K, 1990, FIBONACCI QUART, V28, P72
[7] Euler R, 2005, J INTEGER SEQ, V8
[8] The Number of Independent Sets in a Graph with Small Maximum Degree
Galvin, David
Zhao, Yufei
[J]. GRAPHS AND COMBINATORICS, 2011, 27 (02) : 177 - 186
[9] Golin M., 2005, SIAM, P250
[10] Graphs, partitions and Fibonacci numbers
Knopfmacher, Arnold
Tichy, Robert F.
Wagner, Stephan
Ziegler, Volker
[J]. DISCRETE APPLIED MATHEMATICS, 2007, 155 (10) : 1175 - 1187

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