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arXiv · 2101.04397

On the number of isolate dominating sets of certain graphs

Nima Ghanbari·Saeid Alikhani
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Abstract

Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $S\subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $S$ is an isolate dominating set of $G$, if the induced subgraph $G[S]$ has at least one isolated vertex. The isolate domination number, $\gamma_0(G)$, is the minimum cardinality of an isolate dominating set of $G$. In this paper, we count the number of isolate dominating sets of some specific graphs.

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Nima Ghanbari, Saeid Alikhani. 2021-01-12. On the number of isolate dominating sets of certain graphs. https://arxiv.org/abs/2101.04397

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