n-EDGE-DISTANCE-BALANCED GRAPHS

Abstract

Throughout this paper, we present a new class of graphs so-called n-edge-distance-balanced graphs inspired by the concept of edge-distance-balanced property initially introduced by Tavakoli et al. [Tavakoli M., Yousefi-Azari H., Ashrafi A.R., Note on edge distance-balanced graphs, Trans. Combin. 1 (1) (2012), 1-6].  Moreover, we propose some characteristic results to recognize 2-edge-distance-balanced graphs by using the lack of 2-connectivity in graphs.  Some examples are provided in order to illustrate the obtained conclusions.