PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On quartic half-arc-transitive metacirculants
Dragan Marušič and Primož Šparl
J. algebr. comb. Volume 28, Number 3, pp. 365-395, 2008. ISSN 0925-9899


Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ, where ρ is (m,n)-semiregular for some integers m≥1, n≥2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ 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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8218
Deposited By:Boris Horvat
Deposited On:21 February 2012