On Roman Domination in Middle and Splitting Graphs

Abstract

For a graph G=(V,E), a Roman dominating function(RDF) is a function f:V→{0,1,2} having the property that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. The weight of an RDF ((w(f)) is the sum of assignments for all vertices. The minimum weight of an Roman dominating function on graph G is the Roman domination number, denoted by γ_R (G). In this paper, we study on this variant of the domination number for middle, splitting and Mycielski graphs of some special graphs.