Some distance magic graphs

Abstract

A graph G = ( V , E ) , where | V | = n and | E | = m is said to be a distance magic graph if there exists a bijection from the vertex set V to the set { 1 , 2 , … , n } such that, ∑ v ∈ N ( u ) f ( v ) = k , for all u ∈ V , which is a constant and independent of u , where N ( u ) is the open neighborhood of the vertex u . The constant k is called the distance magic constant of the graph G and such a labeling f is called distance magic labeling of G . In this paper, we present new results on distance magic labeling of C n r and neighborhood expansion D n ( G ) of a graph G . Keywords: Distance magic labeling, Sigma labeling, Circulant graphs