On the Perfect Italian Domination Numbers of Some Graph Classes
Khadija Ben Othman1,*
1Umm Al-Qura University, Mekka, Saudi Arabia
Abstract
A function is called a Perfect Italian dominating function (PIDF) of a graph if for every vertex with . The weight of an PIDF is The minimum weight of all Perfect Italian dominating functions that can be conducted on a graph is called the perfect Italian domination number of and is denoted by . In this paper, we study the problem on different graph classes. We determine the perfect Italian domination numbers of the circulant graphs for and give upper bounds for when . We also find this parameter for generalized Petersen graph when . We determine of strong grids for arbitrary , then we introduce an upper bound for when are arbitraries. Finally, we determine the perfect Italian domination number of Jahangir graph for arbitrary and .
Keywords: perfect Italian dominating function; perfect Italian domination number; Circulant graph; generalized Petersen graph; strong grid; Jahangir graph