Some results on integral sum graphs (Q5948979)

A graph \(G=(V,E)\) is said to be an integral sum graph if its vertices can be given a labeling with distinct integers so that \(uv\in E\) if and only if \(u+v\in V\). The integral sum number of a given graph \(G\) is the smallest number of isolated vertices \(S\) such that \(G\cup S\) is an integral sum graph. The authors study and provide partial solutions to the problem of determining the integral sum number of \(K_n - E(K_r)\) and the complete bipartite graphs \(K_{r,r}\).NEWLINENEWLINENEWLINEThe results of this paper are strongly related to the results of \textit{W. He, Y. Shen, L. Wang, Y. Chang, Q. Kang} and \textit{X. Yu} [Discrete Math. 239, No. 1-3, 137-146 (2001; Zbl 0983.05072)].