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Naslov:On the connectivity of bipartite distance-balanced graphs
Avtorji:ID Miklavič, Štefko (Avtor)
ID Šparl, Primož (Avtor)
Datoteke:URL http://dx.doi.org/10.1016/j.ejc.2011.10.002
 
Jezik:Angleški jezik
Vrsta gradiva:Delo ni kategorizirano
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:IAM - Inštitut Andrej Marušič
Opis:A connected graph Γ is said to be distance-balanced whenever for any pair of adjacent vertices u,v of Γ the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. In [K. Handa, Bipartite graphs with balanced (a,b)-partitions, Ars Combin. 51 (1999), 113-119] Handa asked whether every bipartite distance-balanced graph, that is not a cycle, is 3-connected. In this paper the Handa question is answered in the negative. Moreover, we show that a minimal bipartite distance-balanced graph, that is not a cycle and is not 3-connected, has 18 vertices and is unique. In addition, we give a complete classification of non-3-connected bipartite distance-balanced graphs for which the minimal distance between two vertices in a 2-cut is three. All such graphs are regular and for each k3 there exists an infinite family of such graphs which are k-regular.Furthermore, we determine a number of structural properties that a bipartite distance-balanced graph, which is not 3-connected, must have. As an application, we give a positive answer to the Handa question for the subfamily of bipartite strongly distance-balanced graphs.
Ključne besede:graph theory, connected graphs, connectivity, distance-balanced graphs, bipartite graphs
Leto izida:2012
Št. strani:str. 237-247
Številčenje:Vol. 33, no. 2
PID:20.500.12556/RUP-1686 Povezava se odpre v novem oknu
ISSN:0195-6698
UDK:519.17
COBISS.SI-ID:1024369748 Povezava se odpre v novem oknu
Datum objave v RUP:15.10.2013
Število ogledov:4729
Število prenosov:98
Metapodatki:XML DC-XML DC-RDF
:
MIKLAVIČ, Štefko in ŠPARL, Primož, 2012, On the connectivity of bipartite distance-balanced graphs. [na spletu]. 2012. Vol. 33, no. 2, p. 237–247. [Dostopano 19 marec 2025]. Pridobljeno s: http://dx.doi.org/10.1016/j.ejc.2011.10.002
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