(a,d)-1-Vertex-antimagic vertex labeling

Abstract

In this paper we introduce a new labeling of a graph. We define an (a, d)-1-vertex-antimagic vertex labeling of a graph with p vertices and q edges as a one-to-one mapping taking the vertices onto the integers 1,2,...,p so that the set of vertex-weights of the vertices is equal to (a, a + d,..., a +(p-1)d), where a and d are two fixed positive integers. We study properties of this labeling and construct labelings for some regular graphs.