On the number of outer connected dominating sets of graphs

Abstract

Let G =(V, E) be a simple graph. A set S ⊆ V(G) is called an outerconnected dominating set(or ocd-set) of G, if S is a dominating set of G and either S = V(G) or V\S is a connected graph. In this paper we introduce a polynomial which its coefficients are the number of ocd-sets of G. We obtain some properties of this polynomial and its coefficients. Also we compute this polynomial for some specific graphs.