2017/02/17 by Miklavic, Stefko, Sparl, Primoz
#05C12 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1702.05257
Let ℓ denote a positive integer. A connected graph \G of diameter at least ℓ is said to be ℓ\it -distance-balanced whenever for any pair of vertices u,v of \G such that d(u,v)=ℓ, the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. In this paper we present some basic properties of ℓ-distance-balanced graphs and study in more detail ℓ-distance-balanced graphs of diameter at most 3. We also investigate the ℓ-distance-balanced property of some well known families of graphs such as the generalized Petersen graphs.