A further study on edge-distance-balanced property of the generalized Petersen graphs GP(6n+8, 3)

Abstract

A graph G is said to be edge-distance-balanced if for any edge uν of G, the number of edges closer to u than to ν is equal to the number of edges closer to ν than to u. Let GP(n, k) be a generalized Petersen graph. It is proven that for any integers n≥2, the generalized Petersen graph GP(6n+8, 3) is not edge-distance-balanced.

Subject Classification:

• 05C38
• 05C12

Keywords:

• Edge-distance-balanced graph
• Generalized Petersen graph
• Distance-balanced graph