2-Edge Distance-Balanced Graphs
Combinatorics
2023-09-07 v1
Abstract
In a graph A, for each two arbitrary vertices g, h with d(g,h)=2,|MAg2h|=mAg2h is introduced the number of edges of A that are closer to g than to h. We say A is a 2-edge distance-balanced graph if we have mAg2h=mAh2g. In this article, we verify the concept of these graphs and present a method to recognize k-edge distance-balanced graphs for k = 2,3 using existence of either even or odd cycles. Moreover, we investigate situations under which the Cartesian and lexicographic products lead to 2-edge distance -balanced graphs. In some subdivision-related graphs 2-edge distance-balanced property is verified.
Keywords
Cite
@article{arxiv.2309.02565,
title = {2-Edge Distance-Balanced Graphs},
author = {Zohreh Aliannejadi and Mehdi alaeiyan and Alireza Gilani and Jafar Asadpour},
journal= {arXiv preprint arXiv:2309.02565},
year = {2023}
}