Domination polynomials of k-tree related graphs

Abstract

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G,x)={\sum }_{i=\gamma (G)}^{n}d(G,i)x^i$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $\gamma (G)$ 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 kind of graphs, whose domination polynomial have no nonzero real roots.