The strongly distance-balanced property of the generalized Petersen graphs

Authors

  • Klavdija Kutnar University of Primorska
  • Aleksander Malnič University of Ljubljana
  • Dragan Marušič University of Primorska, University of Ljubljana
  • Štefko Miklavič University of Primorska

DOI:

https://doi.org/10.26493/1855-3974.75.895

Keywords:

graph, strongy distance-balanced, generalized Petersen graph

Abstract

A graph X is said to be strongly distance-balanced whenever for any edge uv of X and any positive integer i, the number of vertices at distance i from u and at distance i + 1 from v is equal to the number of vertices at distance i + 1 from u and at distance i from v. It is proven that for any integers k ≥ 2 and nk2 + 4k + 1, the generalized Petersen graph GP(n, k) is not strongly distance-balanced.

Published

2009-01-25

Issue

Section

Articles