Some families of graphs whose domination polynomials are unimodal

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 $G$. It is conjectured that the domination polynomial of any graph is unimodal. In this paper we present some families of graphs whose domination polynomials are unimodal.

This paper has been withdrawn by the author due to the following error. I regret to announce that Theorem 3 of that paper is incorrect as stated. The product of two symmetric and unimodal polynomials is symmetric and unimodal. It is not true that the product of two unimodal polynomials is unimodal

References in corpus (1)

• Recurrence relations and splitting formulas for the domination polynomial