Dominating Sets and Domination Polynomials of Cycles

• Main Authors: Alikhania, Saeid, Yee-hock, Peng
• Format: Article
• Language: English; English
• Published: 2008
• Online Access: http://psasir.upm.edu.my/id/eprint/7111/1/136.pdf; http://psasir.upm.edu.my/id/eprint/7111/; http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.3268v1.pdf

Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of G, if every vertex in V \S is adjacent to at least one vertex in S. Let Ci n be the family of dominating sets of a cycle Cn with cardinality i, and let d(Cn, i) = |Ci n|. In this paper, we construct Ci n,and obtain a recursive formula for d(Cn, i). Using this recursive formula, we consider the polynomial D(Cn, x) = Pn i=⌈ n 3 ⌉ d(Cn, i)xi, which we call domination polynomial of cycles and obtain some properties of this polynomial.