On the number of outer connected dominating sets of graphs

Saeid Alikhani; Mohammad H. Akhbari; C. Eslahchi; Roslan Hasni

On the number of outer connected dominating sets of graphs

Combinatorics 2024-02-19 v3

Authors: Saeid Alikhani , Mohammad H. Akhbari , C. Eslahchi , Roslan Hasni

Abstract

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.

Keywords

outer-connected dominating set graph polynomial dominating set connected graph graph enumeration

Cite

@article{arxiv.1112.0846,
  title  = {On the number of outer connected dominating sets of graphs},
  author = {Saeid Alikhani and Mohammad H. Akhbari and C. Eslahchi and Roslan Hasni},
  journal= {arXiv preprint arXiv:1112.0846},
  year   = {2024}
}

Comments

9 pages-This paper has published in Utilitas Math. 91 (2013), pp. 99-107

On the number of outer connected dominating sets of graphs

Abstract

Keywords

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