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 se...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.展开更多
文摘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.
