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Naslov:Distance-balanced graphs: Symmetry conditions
Avtorji:Kutnar, Klavdija (Avtor)
Malnič, Aleksander (Avtor)
Marušič, Dragan (Avtor)
Miklavič, Štefko (Avtor)
Datoteke:URL http://dx.doi.org/10.1016/j.disc.2006.03.066
 
Jezik:Angleški jezik
Vrsta gradiva:Delo ni kategorizirano
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:IAM - Inštitut Andrej Marušič
Opis:A graph ▫$X$▫ is said to be distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫, the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. A graph ▫$X$▫ is said to be strongly distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫ and any integer ▫$k$▫, the number of vertices at distance ▫$k$▫ from ▫$u$▫ and at distance ▫$k+1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$k+1$▫ from ▫$u$▫ and at distance ▫$k$▫ from ▫$v$▫. Exploring the connection between symmetry properties of graphs and the metric property of being (strongly) distance-balanced is the main theme of this article. That a vertex-transitive graph is necessarily strongly distance-balanced and thus also distance-balanced is an easy observation. With only a slight relaxation of the transitivity condition, the situation changes drastically: there are infinite families of semisymmetric graphs (that is, graphs which are edge-transitive, but not vertex-transitive) which are distance-balanced, but there are also infinite families of semisymmetric graphs which are not distance-balanced. Results on the distance-balanced property in product graphs prove helpful in obtaining these constructions. Finally, a complete classification of strongly distance-balanced graphs is given for the following infinite families of generalized Petersen graphs: GP▫$(n,2)$▫, GP▫$(5k+1,k)$▫, GP▫$(3k 3,k)$▫, and GP▫$(2k+2,k)$▫.
Ključne besede:graph theory, graph, distance-balanced graphs, vertex-transitive, semysimmetric, generalized Petersen graph
Leto izida:2006
Št. strani:str. 1881-1894
Številčenje:Vol. 306, iss. 16
ISSN:0012-365X
UDK:519.17
COBISS_ID:1714391 Povezava se odpre v novem oknu
Število ogledov:1734
Število prenosov:31
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
Področja:Gradivo ni uvrščeno v področja.
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Skupna ocena:(0 glasov)
Vaša ocena:Ocenjevanje je dovoljeno samo prijavljenim uporabnikom.
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Sekundarni jezik

Jezik:Angleški jezik
Ključne besede:teorija grafov, razdaljno uravnoteženi grafi, polsimetrični grafi, posplošeni Petersenov graf, tranzitivni grafi

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