On the independent domination polynomial of a graph

Abstract

An independent dominating set of the simple graph G=(V,E) is a vertex subset that is both dominating and independent in G. The independent domination polynomial of a graph G is the polynomial Di(G,x)=∑Ax|A|, summed over all independent dominating subsets A⊆V. A root of Di(G,x) is called an independence domination root. We investigate the independent domination polynomials of some generalized compound graphs. As consequence, we construct graphs whose independence domination roots are real. Also, we consider some graphs related to paths and study the number of their independent dominating sets.