On distance-balanced generalized Petersen graphs
Gang Ma, Jianfeng Wang, Sandi Klav\v{z}ar

TL;DR
This paper investigates the distance-balanced properties of generalized Petersen graphs, proving that for sufficiently large n relative to k, these graphs are distance-balanced at their diameter and determining their diameter.
Contribution
It proves that generalized Petersen graphs are diameter-distance-balanced for large n relative to k and determines their diameter in this regime, partially confirming a prior conjecture.
Findings
GP(n,k) is diameter-distance-balanced for large n relative to k
The diameter of GP(n,k) is determined for large n
Partial confirmation of Miklavič and Šparl's conjecture
Abstract
A connected graph of diameter is -distance-balanced if for every with , where is the set of vertices of that are closer to than to . We prove that the generalized Petersen graph is -distance-balanced provided that is large enough relative to . This partially solves a conjecture posed by Miklavi\v{c} and \v{S}parl \cite{Miklavic:2018}. We also determine when is large enough relative to .
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Taxonomy
TopicsAdvanced Graph Theory Research · VLSI and FPGA Design Techniques · Complexity and Algorithms in Graphs
