On the number of isolate dominating sets of certain graphs

2021/01/12 by Nima Ghanbari, Ghanbari, Nima, ‎Saeid Alikhani +1
Computer Science · Neuroscience · #05C15 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Nuclear Receptors and Signaling

paper · pdf · doi:10.48550/arxiv.2101.04397

openalex publication_date 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G=(V,E) be a simple graph. A dominating set of G is a subset S⊆ 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 γ(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, γ₀(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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