More on Perfect Roman Domination in Graphs

Leonard Mijares Paleta, Ferdinand Paler Jamil

Abstract

A perfect Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {0, 1, 2} for which each u ∈ V (G) with f(u) = 0 is adjacent to exactly one vertex v ∈ V (G) with f(v) = 2. The weight of a perfect Roman dominating function f is the value ωG(f) = Pv∈V (G) f(v). The perfect Roman domination number of G is the minimum weight of a perfect Roman dominating function on G. In this paper, we study the perfect Roman domination numbers of graphs under some binary operation

Keywords

Roman dominating function, perfect Roman dominating function, Roman domination number,perfect Roman domination number

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