Abstract

An edge Italian dominating function (EIDF) of a graph $G=(V,E)$ is a function $f:E(G)\rightarrow\{0,1,2\}$ 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 $z_1,z_2$ with$f(z_1)=f(z_2)=1$. The weight of an edge Italian dominating function is the sum $\sum_{x\in E(G)}f(x)$ and the minimum weight of an edge Italian dominating function of $G$ is called the edge Italian domination number of $G$ and is denoted by $\gamma_I^{\textquotesingle} (G)$. In this paper, we determine the edge Italian domination number of some graph products.

Keywords and Phrases

Edge Italian Domination, Edge Italian dominating function, Edge Italian Domination number.

A.M.S. subject classification

05C.

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