# University Calendar

## Minimum Degree of Certain Integral Sum Graphs

Haiying Wang, China University of Geosciences and University of Mississippi

**Abstract**

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.