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Indexed by:期刊论文

Date of Publication:2011-10-01

Journal:ARS COMBINATORIA

Included Journals:Scopus、SCIE

Volume:102

Page Number:483-492

ISSN No.: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.