Generalized k-Rainbow and Generalized ۲-Rainbow Domination in Graphs

Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:

JR_GADM-8-1_004

تاریخ نمایه سازی: 27 شهریور 1403

Abstract:

Assume we have a set of k colors and to each vertex of a graph G we assign an arbitry of these colors. If we require that each vertex to set is assigned has in its closed neighborhood all k colors, then this is called the generalized k-rainbow dominating function of a graph G. The corresponding γgkr, which is the minimum sum of numbers of assigned colores over all vertices of G, is called the gk-rainbow domination number of G. In this paper we present a linear algorithms for determining a minimum generalized ۲-rainbow dominating set of a tree and on GP(n,۲).

Authors

Gholam Hassan Shirdel

University of Qom

Mojtaba Ghanbari

Department of Mathematics, Farahan Branch, Islamic Azad University Farahan, Iran.

Mitra Ramezani

Department of Mathematics, Faculty of Sciences, University of Qom Qom, IRAN.