EDGE ITALIAN DOMINATION IN GRAPHS

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 33

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 $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$ or at least two edges $e_1, e_2$ with $f(e_1)=f(e_2)=1.$ The weight of an edge Italian dominating function is $\sum_{e\in E(G)}f(e)$. The edge Italian domination number of a graph $G$ is defined as the minimum weight of an edge Italian dominating function of $G$ and is denoted by $\gamma_I'(G)$. In this paper, we initiate a study on the edge Italian domination in graphs.

Keywords and Phrases

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

A.M.S. subject classification

05C70.

.....

Download PDF 33 Click here to Subscribe now