Abstract
Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ, where ρ is (m,n)-semiregular for some integers m≥1, n≥2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ 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.
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Both authors were supported in part by “ARRS – Agencija za znanost Republike Slovenije”, program no. P1-0285.
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Marušič, D., Šparl, P. On quartic half-arc-transitive metacirculants. J Algebr Comb 28, 365–395 (2008). https://doi.org/10.1007/s10801-007-0107-y
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DOI: https://doi.org/10.1007/s10801-007-0107-y