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Title: The strongly distance-balanced property of the generalized Petersen graphs Kutnar, Klavdija (Author)Malnič, Aleksander (Author)Marušič, Dragan (Author)Miklavič, Štefko (Author) http://amc.imfm.si/index.php/amc/article/viewFile/75/59 English Not categorized 1.01 - Original Scientific Article IAM - Andrej Marušič Institute 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. graph, strongy distance-balanced, generalized Petersen graph 2009 str. 41-47 Vol. 2, no. 1 1855-3966 519.17 1024077396 1510 68 Document is not linked to any category.

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## Secondary language

Language: English teorija grafov, graf, krepko razdaljno uravnotežen, posplošeni Petersenov graf