ǂThe ǂstrongly distance-balanced property of the generalized Petersen graphs

Klavdija Kutnar (Author), Aleksander Malnič (Author), Dragan Marušič (Author), Štefko Miklavič (Author)

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

Keywords

teorija grafov;graf;krepko razdaljno uravnotežen;posplošeni Petersenov graf;graph;strongy distance-balanced;generalized Petersen graph;

Data

Language:	English
Year of publishing:	2009
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	519.17
COBISS:	1024077396
ISSN:	1855-3966
Parent publication:	Ars mathematica contemporanea
Views:	2928
Downloads:	132
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary keywords:	teorija grafov;graf;krepko razdaljno uravnotežen;posplošeni Petersenov graf;
Type (COBISS):	Not categorized
Pages:	str. 41-47
Volume:	ǂVol. ǂ2
Issue:	ǂno. ǂ1
Chronology:	2009
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;combinatorial analysis;graph theory;kombinatorika;
ID:	14092544