Some standard results on even sum graphs

Abstract

A sum graph is a graph for which there is a labeling of its vertices with distinct positive integers so that two vertices are adjacent if and only if the sum of their labels is the label of another vertex. Integral sum graphs are defined similarly, except that the labels may be any integers. The concept of Even Sum Graphs was introduced by C. David Raj, et al. A graph \(G\) is called an even sum graph if there is a labeling \(\theta\) of its vertices with distinct non - negative even integers, so that for any two distinct vertices \(u\) and \(v, u v\) is an edge of \(G\) if and only if \(\theta(u)+\theta(v)=\theta(w)\) for some vertex \(w\) in \(G\). The minimum number of isolated vertices required to make the graph \(G\), an even sum graph is called the even sum number of \(\mathrm{G}\) and is denoted by \(\gamma(G)\).