 On the [1,2]-domination number of generalized Petersen graphsLily Chen, Yingbin Ma, Yongtang Shi and Yan Zhao Applied Mathematics and Computation, 2018, vol. 327, issue C, 1-7 Abstract: A dominating set in a graph G=(V,E) is a subset S of V such that N[S]=V, that is, each vertex of G either belongs to S or is adjacent to at least one vertex in S. The minimum cardinality of a dominating set in G is called the domination number, denoted by γ(G). A subset S of V is a [1,2]-set if, for every vertex v ∈ V∖S, v is adjacent to at least one but no more than two vertices in S. The [1,2]-domination number of a graph G, denoted by γ[1, 2](G), is the minimum cardinality of a [1, 2]-set of Chellali et al. gave some bounds for γ[1, 2](G) and proposed the following problem: which graphs satisfy γ(G)=γ[1,2](G). Ebrahimi et al. determined the exact value of the domination number for generalized Petersen graphs P(n, k) when k ∈ {1, 2, 3}. In this paper, we determine the exact values of γ[1, 2](P(n, k)) for k ∈ {1, 2, 3}. We also show that γ[1,2](P(n,k))=γ(P(n,k)) for k=1 and k=3, respectively, while for k=2,γ[1, 2](P(n, k)) ≠ γ(P(n, k)) except for n=6,7,9,12. Keywords: Domination number; [1,2]-domination number; Generalized Petersen graph (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:327:y:2018:i:c:p:1-7 DOI: 10.1016/j.amc.2018.01.013 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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