Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2011-10-01

Journal: ARS COMBINATORIA

Included Journals: SCIE、Scopus

Volume: 102

Page Number: 483-492

ISSN: 0381-7032

Key Words: Domination; 2-Rainbow domination; Generalized Petersen graph

Abstract: Assume we have a set of k colors and we assign an arbitrary subset of these colors to each vertex of a graph G. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this assignment is called the k-rainbow dominating function of a graph G. The minimum sum of numbers of assigned colors over all vertices of G, denoted as gamma(rk)(G), is called the k-rainbow domination number of G. In this paper, we prove that gamma(r2)(P(n, 3)) >= inverted right perpendicular 7n inverted left perpendicular.