20.500.12556/RUP-1311 On quartic half-arc-transitive metacirculants 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 matematika teorija grafov metacikličen graf poltranzitiven graf tesno speti grafi grupa avtomorfizmov true true false Angleški jezik Angleški jezik Delo ni kategorizirano 2013-10-15 12:05:48 2013-10-15 12:05:48 2024-03-01 12:00:30 0000-00-00 00:00:00 2008 0 0 str. 365-395 no. 3 Vol. 28 2008 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0925-9899 519.17 14625113 http://dx.doi.org/10.1007/s10801-007-0107-y 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=1311 Inštitut Andrej Marušič 0 0 0