Independent Roman domination in edge corona graphs

Abstract

Let f : V (G) → {0, 1, 2} be a function defined on a graph G with vertex set V (G). For each i ∈ {0, 1, 2}, let Vi = {v ∈ V (G) : f (v) = i}. The function f is called an independent Roman dominating function on G if V1 ∪ V2 is an independent set of G and every vertex in V0 is adjacent to at least one vertex in V ₂. The weight of f is defined as . The independent Roman domination number of G, denoted by i R (G), is the minimum weight among all independent Roman dominating functions on G. In this paper, we study this parameter in the edge corona product graph G ⋄ H of two graphs G and H . Specifically, we establish tight bounds for i _R (G ⋄ H ) in terms of invariants of the factor graphs G and H. Furthermore, we derive closed formulas for i R (G ⋄ H ) for some well-known families of graphs G.