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Title: On quartic half-arc-transitive metacirculants Marušič, Dragan (Author)Šparl, Primož (Author) http://dx.doi.org/10.1007/s10801-007-0107-y English Not categorized 1.01 - Original Scientific Article IAM - Andrej Marušič Institute 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. mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group 2008 str. 365-395 Vol. 28, no. 3 0925-9899 519.17 14625113 1699 62 Document is not linked to any category.

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## Secondary language

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

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