Some distance magic graphs

Abstract

A graph , where and is said to be a distance magic graph if there exists a bijection from the vertex set to the set such that, , for all , which is a constant and independent of , where is the open neighborhood of the vertex . The constant is called the distance magic constant of the graph and such a labeling is called distance magic labeling of . In this paper, we present new results on distance magic labeling of and neighborhood expansion of a graph .

Keywords

• distance magic labeling
• sigma labeling
• circulant graphs