Counting the number of weakly connected dominating sets of graphs

Saeid Alikhani; Somayeh Jahari; Mohammad Mehryar

Counting the number of weakly connected dominating sets of graphs

Combinatorics 2017-03-06 v2

Authors: Saeid Alikhani , Somayeh Jahari , Mohammad Mehryar

Abstract

Let $G=(V(G),E(G))$ be a simple graph. A non-empty set $S\subseteq V (G)$ is a weakly connected dominating set in $G$ , if the subgraph obtained from $G$ by removing all edges each joining any two vertices in $V (G)\setminus S$ is connected. In this paper, we consider some graphs and study the number of their weakly connected dominating sets.

Keywords

weakly connected dominating set dominating set simple graph counting connected subgraph graph theory

Cite

@article{arxiv.1412.8138,
  title  = {Counting the number of weakly connected dominating sets of graphs},
  author = {Saeid Alikhani and Somayeh Jahari and Mohammad Mehryar},
  journal= {arXiv preprint arXiv:1412.8138},
  year   = {2017}
}

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9 pages, 2 Figures

Counting the number of weakly connected dominating sets of graphs

Abstract

Keywords

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