A STUDY ON 3-RAINBOW DOMINATION NUMBER OF SOME SPECIAL CLASSES OF GRAPHS
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Published:
Jul 28, 2017
Keywords:
Domination, Domination number, k-rainbow domination number, 3-rainbow domination, number, wheel graph, Triangular snake graph, Double triangular snake graph, n-Barbell graph, n-Sunlet graph, n-Centipede graph, Crown graph, Clebsch graph, Intercon
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Abstract
For a given simple, finite, connected and undirected graph G= (V,E) and a set of k-colours numbered 1,2,3,…k, the 3-rainbow domination is defined as a mapping f : V(G)→þ{1,2,3} such that for all v∈V(G) with f(v)=ϕ⋃_(u∈N(v))▒〖f(u)={1,2,3} 〗Such function is called a 3-rainbow domination function (3RDF) and the minimum weight of such function is called the 3-rainbow domination number of G and is denoted by γ_r3(G). In this paper, we obtained the 3-rainbow domination number of some special graphs. Here [x]-denote the integral part of x, ⌈x⌉ denote the upper integral part of x and denote the lower integral part of x.
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