Let [n]~* denote the set of integers{-n-1/2,n-21, isodd, and ,n/2} {0} if n is even. A super edge-graceful labeling f of agraph G of order p and size q is a bijection f : E(G) [q]~*,such that the induced vertex labeling f~*given byf~*(u) = Σ_(uve)E(G) f(uv) is a bijection f~* : V (G)[p]~*.A graph is super edge-graceful if it has asuper edge-graceful labeling. We show by construction that all completebipartite graphs are super edge-graceful except for K_(2,2), K_(2,3),andK_(1,n)if n is odd.
展开▼
