Edge distance-balanced of Hamming graphs

Abstract

A nonempty graph is called nicely distance-balanced, respectively, edge distance-balanced, whenever there exist positive integers γ_V and γ_E, such that for any two adjacent vertices u, v of Γ, there are exactly γ_V vertices of Γ, respectively γ_E edges of Γ, which are closer to v than u. In this paper, we show that Hamming graphs H(n, q) are both nicely distance-balanced and nicely edge distance-balanced.

Subject Classification: (2010):

• 05C15

Keywords:

• Nicely distance-balanced
• Nicely edge distance-balanced
• Hamming graphs