On nicely distance-balanced of folded cube graphs

A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ_V (γ_E), such that for any adjacent vertices u and v in V(Γ), there are exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ) that are closer to u than v, and exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ)) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ_V (γ_E), such that for any adjacent vertices u and v in V(Γ), there are exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ) that are closer to u than v, and exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ)) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.