On quartic half-arc-transitive metacirculants

Marušič, Dragan ; Šparl, Primož

Journal of Algebraic Combinatorics, Tome 28 (2008) no. 3, pp. 365-395.

Résumé

Summary: 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 $m\geq 1, n\geq 2$, 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.

Détail

Classification : transitive, graphs, is, given, in, [20], for, odd, radius, and, in, [29], for, even, radius
Keywords: keywords graph, metacirculant graph, half-arc-transitive, tightly attached, automorphism group