On the number of outer connected dominating sets of graphs

Details On the number of outer connected dominating sets of graphs On the number of outer connected dominating sets of graphs

2011-12-05

arxiv.org/abs/1112.0846v2

Mathematics

Combinatorics

1 page

Scientific paper

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V(G)$ is called an outer-connected dominating set (or ocd-set) of $G$, if $S$ is a dominating set of $G$ and either $S=V(G)$ or $V\backslash S$ 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.

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