Rainbow domination numbers of generalized Petersen graphs

Zhipeng Gao, Hui Lei and Kui Wang

Applied Mathematics and Computation, 2020, vol. 382, issue C

Abstract: Domination and its variations in graphs are natural models for the location problems in operations research. In this paper, we investigate the rainbow domination number of graphs, which was introduced by Brešar, Henning and Rall. Given a graph G and a positive integer t, a t-rainbow dominating function of G is a function f from vertex set to the set of all subsets of {1, 2, ⋅⋅⋅, t} such that for any vertex v with f(v)=ϕ, we have ⋃u∈N(v)f(u)={1,2,⋯,t}. The t-rainbow domination problem is to determine the t-rainbow domination number γrt(G) of G, that is the minimum value of ∑v ∈ V(G)|f(v)|, where f runs over all t-rainbow dominating functions of G. The domination number and its variations of generalized Petersen graphs P(n, k) are widely investigated. The exact values of γr2(P(n, 1)) and γr3(P(n, 1)) are already determined in [11, 12]. In this paper, we determine the exact values of γrt(P(n, 1)) for any t ≥ 8 and t=4 and prove that γrt(P(2k,k))=4k for t ≥ 6, where P(2k, k) is a special graph.

Keywords: Rainbow domination number; Generalized Petersen graphs (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303076

DOI: 10.1016/j.amc.2020.125341

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