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On quartic half-arc-transitive metacirculantsMarušič, Dragan ; Šparl, PrimožFollowing 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.Source: Journal of algebraic combinatorics. - ISSN 0925-9899 (Vol. 28, no. 3, 2008, str. 365-395)Type of material - article, component partPublish date - 2008Language - englishCOBISS.SI-ID - 14625113
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Marušič, Dragan | 02887 |
Šparl, Primož | 23341 |
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