On 1-vertex bimagic vertex labeling

Abstract

A 1-vertex magic vertex labeling of a graph G with p vertices is defined as a bijection f from the vertices to the integers 1,2, . . ., p with the property that there is a constant k such that at any vertex x, y∈N(x)f (y) = k, where N (x) is the set of vertices adjacent to x. In this paper we introduce 1-vertex bimagic vertex labeling of a graph G and obtain the necessary condition for a graph to be 1-vertex bimagic. We exhibit the same type of labeling for some class of graphs and give some general results.