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On quartic half-arc-transitive metacirculantsDragan Marušič,

Primož Šparl, 2008, original scientific article

**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.

**Found in:** ključnih besedah

**Summary of found:** ...and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It...

**Keywords:** mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group

**Published:** 15.10.2013; **Views:** 1700; **Downloads:** 62

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