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:	3818
Downloads:	132
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