On Edge-Antimagic Graph Labeling and Associated Deficiency Numbers

摘要

An edge-antimagic vertex labeling of a finite simple undirected graph G = (V, E) with p vertices is an injective mapping f : V {1,2, ,p} such that the induced edge weightings are pairwise distinct, where the induced weighting over the edge uv is f(u) f(v). The edge-antimagic vertex deficiency number p(G) of a graph C, which is the minimum integer k such that G is edge-antimagic by relaxing the range of the injective vertex labeling f from {1, 2, ..., p} to {1,2, ,p k}. In this article, we study the related edge-antimagic vertex labeling and deficiency numbers of complete bipartite graphs and complete graphs.