Super edge-graceful labelings of complete bipartite graphs.

Let [n]∗ denote the set of integers {−n−1 2 , . . . , n−1 2 } if n is odd, and {−n 2 , . . . , n 2 } \ {0} if n is even. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) → [q]∗, such that the induced vertex labeling f ∗ given by f ∗(u) = ∑ uv E(G) f(uv) is a bijection f ∗ : V (G) → [p]∗. A graph is super edge-graceful if it has a super edge-graceful labeling. We show by construction that all complete bipartite graphs are super edge-graceful except for K2,2, K2,3, and K1,n if n is odd. ∗ Research supported by NSF Grant DMS0648919, University of West Georgia 242 A. KHODKAR, S. NOLEN AND J.T. PERCONTI