The strongly distance-balanced property og the generalized Petersen graphs - Kutnar, Klavdija (Ars mathematica contemporanea, 2009)
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.
Keywords: grafi; teorija grafov