The strongly distance-balanced property of the generalized Petersen graphs

Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič

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.

Keywords


graph; strongy distance-balanced; generalized Petersen graph

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

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications