A note on edge-distance-balanced property of the generalized Petersen graphsGP(4t, 2)
Mahboubeh Ezadi, Mehdi Alaeiyan · Journal of Discrete Mathematical Sciences and Cryptography · 2019
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.