[1,2]-Domination in Generalized Petersen Graphs

2019/06/27 by Beggas, Fairouz, Turau, Volker, Haddad, Mohammed +1
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.11966

Abstract

A vertex subset S of a graph G=(V,E) is a [1,2]-dominating set if each vertex of V\backslash S is adjacent to either one or two vertices in S. The minimum cardinality of a [1,2]-dominating set of G, denoted by γ_[1,2](G), is called the [1,2]-domination number of G. In this paper the [1,2]-domination and the [1,2]-total domination numbers of the generalized Petersen graphs P(n,2) are determined.

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