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On the number of closed walks in vertex-transitive graphsJajcay, Robert ; Malnič, Aleksander ; Marušič, DraganThe results of Širáň and the first author [A construction of vertex-transitive non-Cayley graphs, Australas. J. Combin. 10 (1994) 105-114; More constructions of vertex-transitive non-Cayley graphs ... based on counting closed walks, Australas. J. Combin. 14 (1996) 121-132] are generalized, and new formulas for the number of closed walks of length ▫$p^r$▫ or ▫$pq$▫, where ▫$p$▫ and ▫$q$▫ are primes, valid for all vertex-transitive graphs are found. Based on these formulas, several simple tests for vertex-transitivity are presented, as well as lower bounds on the orders of the smallest vertex- and arc-transitive groups of automorphisms for vertex-transitive graphs of given valence.Source: Discrete mathematics. - ISSN 0012-365X (Vol. 307, iss. 3-5, 2007, str. 484-493)Type of material - article, component partPublish date - 2007Language - englishCOBISS.SI-ID - 14181209
Author
Jajcay, Robert |
Malnič, Aleksander |
Marušič, Dragan
Topics
matematika |
teorija grafov |
tranzitivnost po točkah |
Cayleyjev graf |
zaprti sprehodi |
cikli |
grupa avtomorfizmov |
mathematics |
graph theory |
vertex-transitive graphs |
Cayley graphs |
closed walks |
cycles |
automorphism groups
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Jajcay, Robert | 37724 |
Malnič, Aleksander | 02507 |
Marušič, Dragan | 02887 |
Source: Personal bibliographies
and: SICRIS
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