A STUDY ON 3-RAINBOW DOMINATION NUMBER OF SOME SPECIAL CLASSES OF GRAPHS

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.