ON DISTANCE IRREGULAR LABELLING OF GRAPHS

Abstract

Motivated by definition of distance magic labelling, we introduce a new type of irregular labelling whose evaluation is based on the neighbourhood of a vertex. We define a distance irregular labelling on a graph G with v vertices to be an assignment of positive integer labels to vertices so that the weights calculated at vertices are distinct. The weight of a vertex x in G is defined to be the sum of the labels of all the vertices adjacent to x. The distance irregularity strength of G, denoted by dis(G), is the minimum value of the largest label over all such irregular assignments.