On quartic half-arc-transitive metacirculants

Marušič, Dragan; Šparl, Primož

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Title:	On quartic half-arc-transitive metacirculants
Authors:	ID Marušič, Dragan (Author) ID Šparl, Primož (Author)
Files:	http://dx.doi.org/10.1007/s10801-007-0107-y
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms $\rho$ and $\sigma$ , where $\rho$ is $(m,n)$ -semiregular for some integers $m \ge 1$ , $n \ge 2▫$, and where ▫$\sigma$ normalizes $\rho$ , cyclically permuting the orbits of $\rho$ in such a way that $\sigma^m$ has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed.
Keywords:	mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group
Year of publishing:	2008
Number of pages:	str. 365-395
Numbering:	Vol. 28, no. 3
PID:	20.500.12556/RUP-1311
ISSN:	0925-9899
UDC:	519.17
COBISS.SI-ID:	14625113
Publication date in RUP:	15.10.2013
Views:	4958
Downloads:	135
Metadata:
:	MARUŠIČ, Dragan and ŠPARL, Primož, 2008, On quartic half-arc-transitive metacirculants. [online]. 2008. Vol. 28, no. 3, p. 365–395. [Accessed 28 March 2025]. Retrieved from: http://dx.doi.org/10.1007/s10801-007-0107-y Copy citation