Arc-transitive cycle decompositions of tetravalent graphs

Miklavič, Štefko; Potočnik, Primož; Wilson, Steve

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Title:	Arc-transitive cycle decompositions of tetravalent graphs
Authors:	ID Miklavič, Štefko (Author) ID Potočnik, Primož (Author) ID Wilson, Steve (Author)
Files:	http://dx.doi.org/10.1016/j.jctb.2008.01.005
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	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.
Keywords:	mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Year of publishing:	2008
Number of pages:	str. 1181-1192
Numbering:	Vol. 98, no. 6
PID:	20.500.12556/RUP-3883
ISSN:	0095-8956
UDC:	519.17
COBISS.SI-ID:	14627417
Publication date in RUP:	15.10.2013
Views:	4761
Downloads:	88
Metadata:
:	MIKLAVIČ, Štefko, POTOČNIK, Primož and WILSON, Steve, 2008, Arc-transitive cycle decompositions of tetravalent graphs. [online]. 2008. Vol. 98, no. 6, p. 1181–1192. [Accessed 1 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.jctb.2008.01.005 Copy citation