Arc-transitive cycle decompositions of tetravalent graphs

Miklavič, Štefko; Potočnik, Primož; Wilson, Steve

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Naslov:	Arc-transitive cycle decompositions of tetravalent graphs
Avtorji:	ID Miklavič, Štefko (Avtor) ID Potočnik, Primož (Avtor) ID Wilson, Steve (Avtor)
Datoteke:	http://dx.doi.org/10.1016/j.jctb.2008.01.005
Jezik:	Angleški jezik
Vrsta gradiva:	Delo ni kategorizirano
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	IAM - Inštitut Andrej Marušič
Opis:	A cycle decomposition of a graph $\Gamma$ is a set $\mathcal{C}$ of cycles of $\Gamma$ such that every edge of $\Gamma$ belongs to exactly one cycle in $\mathcal{C}$ . Such a decomposition is called arc-transitive if the group of automorphisms of $\Gamma$ that preserve setwise acts transitively on the arcs of $\Gamma$ . In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.
Ključne besede:	mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Leto izida:	2008
Št. strani:	str. 1181-1192
Številčenje:	Vol. 98, no. 6
PID:	20.500.12556/RUP-3883
ISSN:	0095-8956
UDK:	519.17
COBISS.SI-ID:	14627417
Datum objave v RUP:	15.10.2013
Število ogledov:	4752
Število prenosov:	88
Metapodatki:
:	MIKLAVIČ, Štefko, POTOČNIK, Primož in WILSON, Steve, 2008, Arc-transitive cycle decompositions of tetravalent graphs. [na spletu]. 2008. Vol. 98, no. 6, p. 1181–1192. [Dostopano 31 marec 2025]. Pridobljeno s: http://dx.doi.org/10.1016/j.jctb.2008.01.005 Kopiraj citat