Affiliation:
1. Department of Mathematics, Yazd University, Yazd 89195-741, Iran
Abstract
Let G be a simple graph of order n. The domination polynomial of G is the polynomial DG,x=∑i=γ(G)nd(G,i)xi, where d(G, i) is the number of dominating sets of G of size i and γ(G) is the domination number of G. In this paper, we study the domination polynomials of several classes of k-tree related graphs. Also, we present families of these kinds of graphs, whose domination polynomials have no nonzero real roots.