On the $n-$dominating graph of specific graphs

Saeid Alikhani; Davood Fatehi

On the $n-$dominating graph of specific graphs

Combinatorics 2015-03-02 v2

Authors: Saeid Alikhani , Davood Fatehi

Abstract

Let $G=(V,E)$ be a graph. A set $S\subseteq V(G)$ is a dominating set, if every vertex in $V(G)\backslash S$ is adjacent to at least one vertex in $S$ . The $k$ -dominating graph of $G$ , $D_k (G)$ , is defined to be the graph whose vertices correspond to the dominating sets of $G$ that have cardinality at most $k$ . Two vertices in $D_k(G)$ are adjacent if and only if the corresponding dominating sets of $G$ differ by either adding or deleting a single vertex. In this paper we consider and study the $n$ -dominating graph of specific graphs.

Keywords

dominating set k-dominating graph graph reconfiguration combinatorics vertex deletion vertex addition

Cite

@article{arxiv.1410.1169,
  title  = {On the $n-$dominating graph of specific graphs},
  author = {Saeid Alikhani and Davood Fatehi},
  journal= {arXiv preprint arXiv:1410.1169},
  year   = {2015}
}

Comments

15 pages, 6 figures. This is a new version of paper entitled "On the $n-$dominating graph of $K_{n}$"

On the $n-$dominating graph of specific graphs

Abstract

Keywords

Cite

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