Perfect Dominating sets and Perfect Domination Polynomial of a Path
Let be a simple graph. A set is a perfect dominating set of G, if every vertex in is adjacent to exactly one vertex in S. Let be the family of all perfect dominating sets of a path with cardinality , and let . In this paper, we construct for a path with vertices and obtain a recursive formula of . Using this recursive formula, we consider the polynomial , which we call perfect domination polynomial of paths and obtain some properties of this polynomial.