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Title:On quartic half-arc-transitive metacirculants
Authors:Marušič, Dragan (Author)
Šparl, Primož (Author)
Work type:Not categorized
Tipology: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
COBISS_ID:14625113 Link is opened in a new window
Categories:Document is not linked to any category.
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Secondary language

Keywords:matematika, teorija grafov, metacikličen graf, poltranzitiven graf, tesno speti grafi, grupa avtomorfizmov


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