Interior dominating sets and interior domination polynomials of paths

Let G=(V, E) be a undirected simple graph. Let Pn be the path with n vertices and let DId (Pn, i) be the family of interior dominating sets of G with cardinality. Let dId(Pn, i)=∣DId(Pn, i)∣. In this paper, we obtain a recursive formula for dld(Pn, i). Using this recursive formula , we construct the polynomial DId(pn,x)=∑i=|n3|n−2dId(pn,i)xi, which we call interior domination polynomial of Pn and obtain some properties of this polynomial.