On edge-antimagic graph labeling and associated deficiency numbers

Abstract

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) 4-f(v). The edge-antimagic vertex deficiency number fi(G) of a graph (7, which is the minimum integer k such that G is edge-antimagic by relaxing the range of the injective vertex labeling/from {1,2, ••• ,p} to {1,2, •••,;> + k). In this article, we study the related edge-antimagic vertex labeling and deficiency numbers of complete bipartite graphs and complete graphs. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.