A note on edge-distance-balanced property of the generalized Petersen graphs GP(4t, 2)

摘要

A graph G is said to be edge-distance-balanced if for any edge uv 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. Let GP(n, k) be a generalized Petersen graph. It is proven that for any integers t ≥ 5, the generalized Petersen graph GP(4t, 2) is not edge-distance-balanced.