On (a, d)-vertex-antimagic total labeling of Harary graphs

Abstract

Let G = (V, E) be a graph with v vertices and e edges. An (a, d)-vertex-antimagic total labeling is a bijection λ from V(G)U E(G) to the set of consecutive integers 1,2,..., v + e, such that the weights of the vertices form an arithmetic progression with the initial term a and common difference d. If λ (V(G)) = {1, 2,..., v} then we call the labeling a super (a, d) -vertex-antimagic total. In this paper we construct (a, d)-vertex-antimagic total labeling on Harary graphs as well as for the disjoint union of k identical copies of Harary graphs.