TITLE:
Dominating Sets and Domination Polynomials of Square of Paths
AUTHORS:
A. Vijayan, K. Lal Gipson
KEYWORDS:
Domination Set; Domination Number; Domination Polynomials
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.3 No.1,
January
29,
2013
ABSTRACT: 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.