[1,2]-Domination in generalized Petersen graphs

A vertex subset S of a graph G = (V,E) is a [1, 2]-dominating set if each vertex of V 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.

Subjects

Generalized Petersen graph

vertex domination

[ 1, 2 ] -domination

[ 1, 2 ] -total domination

Funding(s)

Fehlertolerante verteilte Algorithmen

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[1,2]-Domination in generalized Petersen graphs