Resumen de On certain regular nicely distance-balanced graphs

Blas Fernández, Stefko Miklavic, Safet Penjić

• A connected graph Γ is called nicely distance-balanced, whenever there exists a positive integer γ = γ(Γ) such that, for any two adjacent vertices u, v of Γ, there are exactly γ vertices of Γ which are closer to u than to v, and exactly γ vertices of Γ which are closer to v than to u. Let d denote the diameter of Γ. It is known that d ≤ γ, and that nicely distance-balanced graphs with γ = d are precisely complete graphs and cycles of length 2d or 2d + 1. In this paper we classify regular nicely distance-balanced graphs with γ = d + 1.