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 ?$k \ge 2$? and ?$n \ge k^2 + 4k + 1$?, the generalized Petersen graph GP?$(n, k)$? is not strongly distance-balanced.

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URN

URN:NBN:SI:doc-ALT9RRPZ

COBISSID

1024077396

Added

16.12.2021

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Citation

APA:

Kutnar, Klavdija, Malnič, Aleksander, Marušič, Dragan, Miklavič, Štefko (2009). The strongly distance-balanced property og the generalized Petersen graphs. Ars mathematica contemporanea, volume 2, issue 1, str. 41-47. URN:NBN:SI:doc-ALT9RRPZ from http://www.dlib.si

MLA:

Kutnar, Klavdija, Malnič, Aleksander, Marušič, Dragan, Miklavič, Štefko. "The strongly distance-balanced property og the generalized Petersen graphs." Ars mathematica contemporanea volume 2. issue 1 (2009) str. 41-47.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-ALT9RRPZ>

Ars mathematica contemporanea
2008-
(Assembly record)