On quartic half-arc-transitive metacirculants

Dragan Marušič (Author), Primož Šparl (Author)

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

matematika;teorija grafov;metacikličen graf;poltranzitiven graf;tesno speti grafi;grupa avtomorfizmov;mathematics;graph theory;metacirculant graph;half-arc-transitive graph;tightly attached;automorphism group;

Data

Language:	English
Year of publishing:	2008
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.17
COBISS:	14625113
ISSN:	0925-9899
Views:	3622
Downloads:	132
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	matematika;teorija grafov;metacikličen graf;poltranzitiven graf;tesno speti grafi;grupa avtomorfizmov;
Type (COBISS):	Not categorized
Pages:	str. 365-395
Volume:	ǂVol. ǂ28
Issue:	ǂno. ǂ3
Chronology:	2008
DOI:	10.1007/s10801-007-0107-y
ID:	1473510