On integral sum graphs with a saturated vertex

As introduced by F. Harary in 1994, a graph G is said to be an integral sum graph if its vertices can be given a labeling f with distinct integers so that for any two 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 in G. We prove that every integral sum graph with a saturated vertex, except the complete graph K₃, has edge-chromatic number equal to its maximum degree. (A vertex of a graph G is said to be saturated if it is adjacent to every other vertex of G.) Some direct corollaries are also presented.