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Ma, Gang; Wang, Jianfeng; Klavžar, Sandi
Annals of combinatorics, 03/2024, Letnik: 28, Številka: 1Journal Article
A connected graph G of diameter diam ( G ) ≥ ℓ is ℓ -distance-balanced if | W xy | = | W yx | for every x , y ∈ V ( G ) with d G ( x , y ) = ℓ , where W xy 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 diam ( G P ( n , k ) ) -distance-balanced provided that n is large enough relative to k . This partially solves a conjecture posed by Miklavič and Šparl (Discrete Appl Math 244:143–154, 2018). We also determine diam ( G P ( n , k ) ) when n is large enough relative to k .
