Journal article
Electronic Journal of Graph Theory and Applications
• 2018

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. A root of D(G, x) is called a domination root of G. Obviously, 0 is a domination root of every graph G with multiplicity $\gamma(G)$. In the study of the domination roots of graphs, this naturally raises the question: Which graphs have no nonzero real domination roots? In this paper we present some families of graphs whose have this property.