Independence roots and independence fractals of certain graphs

被引：13

作者：

Alikhani S. ^{[1
]}

Peng Y.-H. ^{[2
]}

机构：

[1] Department of Mathematics, Yazd University

[2] Department of Mathematics, University Putra Malaysia

来源：

Journal of Applied Mathematics and Computing | 2011年 / 36卷 / 1-2期

关键词：

Independence fractal; Independence polynomial; Jacobsthal polynomial; Julia set;

D O I：

10.1007/s12190-010-0389-4

中图分类号：

学科分类号：

摘要：

The independence polynomial of a graph G is the polynomial Σi k x k, where i k denote the number of independent sets of cardinality k in G. In this paper, we obtain the relationships between the independence polynomial of path P n and cycle C n with Jacobsthal polynomial. We find all roots of Jacobsthal polynomial. As a consequence, the roots of independence polynomial of the family {P n } and {C n } are real and dense in (-∞,-1/4]. Also we investigate the independence fractals or independence attractors of paths, cycles, wheels and certain trees. © 2010 Korean Society for Computational and Applied Mathematics.

引用

页码：89 / 100

页数：11

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