Dominating Sets and Domination Polynomials of Square of Paths

• 作者: A. Vijayan K. Lal Gipson
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: DOMINATION SET DOMINATION NUMBER DOMINATION POLYNOMIALS
• 年，卷（期）: 2013,（1）
• 页码范围: 60-69
• 页数: 10页
• 分类号: O1

摘要

Let G = (V, E) be a simple graph. A set S í V is a dominating set of G, if every vertex in V-S is adjacent to at least one vertex in S. Let be the square of the Path and let denote the family of all dominating sets of with cardinality i. Let . In this paper, we obtain a recursive formula for . Using this recursive formula, we construct the polynomial, , which we call domination polynomial of and obtain some properties of this polynomial.