Perfect double Italian domination of a graph

Abstract

AbstractFor a graph [Formula: see text] with [Formula: see text] and [Formula: see text], a perfect double Italian dominating function is a function [Formula: see text] having the property that [Formula: see text], for every vertex [Formula: see text] with [Formula: see text]. The weight of a perfect double Italian dominating function f is the sum [Formula: see text] and the minimum weight of a perfect double Italian dominating function on G is the perfect double Italian domination number [Formula: see text] of G. We initiate the study of perfect double Italian dominating functions. We check the [Formula: see text] of some standard graphs and evaluate with γdI of such graphs. The perfect double Italian dominating functions versus perfect double Roman dominating functions are perused. The NP-completeness of this parameter is verified even when it is restricted to bipartite graphs. Finally, we characterize the graphs G of order n with [Formula: see text].

Keywords

• Double Italian domination
• perfect double Italian domination
• perfect double Roman domination
• complexity
• 05C69