2022/08/17 by Gang Ma, Jianfeng Wang, Ma, Gang +3
Computer Science · Engineering · #05C12 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #VLSI and FPGA Design Techniques
paper · pdf · doi:10.48550/arxiv.2208.08305
openalex publication_date 2022/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A connected graph G of diameter \rm diam(G) ≥ ℓ is ℓ-distance-balanced if |Wxy|=|Wyx| for every x,y∈ V(G) with dG(x,y)=ℓ, where Wxy is the set of vertices of G that are closer to x than to y. We prove that the generalized Petersen graph GP(n,k) is \rm diam(GP(n,k))-distance-balanced provided that n is large enough relative to k. This partially solves a conjecture posed by Miklavič and Šparl \citeMiklavic:2018. We also determine \rm diam(GP(n,k)) when n is large enough relative to k.