Some points regarding the edge-distance-balanced property of the generalized Petersen graphs GP(n, 2)

Abstract

Suppose t ≥ 5 denote a positive integer. a graph G of diameter d is said to be edge-distance-balanced whenever for any pair of vertices u, v of G, the number of edges closer to u than to v is equal to the number of edges closer to v than to u. suppose GP(n, 2) be generalized Petersen graph. In this article we consider that for any positive integer t ≥ 5, the generalized Petersen graph GP(4t + 1, 2) GP(4t + 2, 2) GP(4t + 3, 2) are not edge-distance-balanced.