The strongly distance-balanced property of the generalized Petersen graphsKutnar, Klavdija (Avtor) Malnič, Aleksander (Avtor) Marušič, Dragan (Avtor) Miklavič, Štefko (Avtor) graphstrongy distance-balancedgeneralized Petersen graphA 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.20092013-10-15 12:06:32Neznano1901sl