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Naslov:Distance-balanced graphs: Symmetry conditions
Avtorji:ID Kutnar, Klavdija (Avtor)
ID Malnič, Aleksander (Avtor)
ID Marušič, Dragan (Avtor)
ID 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(3k3,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
PID:20.500.12556/RUP-835 Povezava se odpre v novem oknu
ISSN:0012-365X
UDK:519.17
COBISS.SI-ID:1714391 Povezava se odpre v novem oknu
Datum objave v RUP:15.10.2013
Število ogledov:6949
Število prenosov:93
Metapodatki:XML DC-XML DC-RDF
:
KUTNAR, Klavdija, MALNIČ, Aleksander, MARUŠIČ, Dragan in MIKLAVIČ, Štefko, 2006, Distance-balanced graphs: Symmetry conditions. [na spletu]. 2006. Vol. 306, no. 16, p. 1881–1894. [Dostopano 19 marec 2025]. Pridobljeno s: http://dx.doi.org/10.1016/j.disc.2006.03.066
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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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