A Note on Integral Sum Crowns

Abstract

The sum graph of a set \(S\) of positive integers is the graph \(G^+(S)\) having \(S\) as its vertex set, with two vertices adjacent if and only if their sum is in \(S\). A graph \(G\) is called a sum graph if it is isomorphic to the sum graph \(G^+(S)\) of some finite subset \(S\) of \(N\). An integral sum graph is defined just as the sum graph, the difference being that \(S\) is a subset of \(Z\) instead of \(N\). The sum number of a graph \(G\) is defined as the smallest number of isolated vertices when added to \(G\) results in a sum graph. The integral sum number of \(G\) is defined analogously. In this paper, we study some classes of integral sum graphs.