Counting independent sets in Riordan graphs

被引：1

作者：

Cheon, Gi-Sang ^{[1
]}

Jung, Ji-Hwan ^{[2
]}

Kang, Bumtle ^{[1
]}

Kim, Hana ^{[1
]}

Kim, Suh-Ryung ^{[3
]}

Kitaev, Sergey ^{[4
]}

Mojallal, Seyed Ahmad ^{[5
,6
]}

机构：

[1] Sungkyunkwan Univ, Appl Algebra & Optimizat Res Ctr, Dept Math, Suwon 16419, South Korea

[2] Seoul Natl Univ, Ctr Educ Res, Seoul 08826, South Korea

[3] Seoul Natl Univ, Dept Math Educ, Seoul 08826, South Korea

[4] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[5] GERAD, Montreal, PQ H3T 1J4, Canada

[6] HEC Montreal, Montreal, PQ H3T 1J4, Canada

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 11期

基金：

新加坡国家研究基金会;

关键词：

Riordangraph; Toeplitzgraph; Independentset; Pattern avoiding sequence; Fibonacci number; Pell number; Hamiltonian path; CHROMATIC NUMBER; TOEPLITZ;

D O I：

10.1016/j.disc.2020.112043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of a Riordan graph was introduced recently, and it is a far-reaching generalization of the well-known Pascal graphs and Toeplitz graphs. However, apart from a certain subclass of Toeplitz graphs, nothing was known on independent sets in Riordan graphs. In this paper, we give exact enumeration and lower and upper bounds for the number of independent sets for various classes of Riordan graphs. Remarkably, we offer a variety of methods to solve the problems that range from the structural decomposition theorem to methods in combinatorics on words. Some of our results are valid for any graph. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：10

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