Haiying Wang, China University of Geosciences and University of Mississippi
The concept of Integral Sum Graph was introduced by F. Harary in 1994 and since then it has many applications in Computer Science. A graph G is called an integral sum graph if its vertices can be given a labeling f with distinct integers so that for every pair of distinct vertices u and v of G, uv is an edge of G if and only if f(u)+f(v) = f(w) for some vertex w of G. In this talk, I will present my recent work on sum graphs and integral sum graphs regarding relevant conjectures posed by Harary. I will show that for every given positive integer r, there exists a connected integral sum graph with r as the minimum degree. Furthermore, we show an inequality between the order and size of any connected integral sum graph without saturated vertex.