EDGE ITALIAN DOMINATION OF SOME GRAPH PRODUCTS

Abstract

An edge Italian dominating function (EIDF) of agraph G = (V,E) is a function f :E(G) → {0,1,2} such that every edge x with f(x) = 0 is adjacent to some edge y with f(y) = 2 or adjacent to at least two edges z1, z2 with f(z1) = f(z2) = 1. The weight of anedge Italian dominating function is the sum x ∈ E (G) f(x) and the minimum weight of anedge Italian dominating function of  G is called the edge Italian domination number of G and is denoted by γ′ I (G). In this paper, we determine the edge Italian domination number of some graph products.