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Title:Distance-balanced graphs: Symmetry conditions
Authors:ID Kutnar, Klavdija (Author)
ID Malnič, Aleksander (Author)
ID Marušič, Dragan (Author)
ID Miklavič, Štefko (Author)
Files:URL http://dx.doi.org/10.1016/j.disc.2006.03.066
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract: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).
Keywords:graph theory, graph, distance-balanced graphs, vertex-transitive, semysimmetric, generalized Petersen graph
Year of publishing:2006
Number of pages:str. 1881-1894
Numbering:Vol. 306, iss. 16
PID:20.500.12556/RUP-835 This link opens in a new window
ISSN:0012-365X
UDC:519.17
COBISS.SI-ID:1714391 This link opens in a new window
Publication date in RUP:15.10.2013
Views:6953
Downloads:93
Metadata:XML DC-XML DC-RDF
:
KUTNAR, Klavdija, MALNIČ, Aleksander, MARUŠIČ, Dragan and MIKLAVIČ, Štefko, 2006, Distance-balanced graphs: Symmetry conditions. [online]. 2006. Vol. 306, no. 16, p. 1881–1894. [Accessed 19 March 2025]. Retrieved from: http://dx.doi.org/10.1016/j.disc.2006.03.066
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Secondary language

Language:English
Keywords:teorija grafov, razdaljno uravnoteženi grafi, polsimetrični grafi, posplošeni Petersenov graf, tranzitivni grafi


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