| Title: | On quartic half-arc-transitive metacirculants |
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| Authors: | ID Marušič, Dragan (Author)
ID Šparl, Primož (Author) |
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| Files: |  http://dx.doi.org/10.1007/s10801-007-0107-y
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| 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. |
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| Keywords: | mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group |
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| Year of publishing: | 2008 |
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| Number of pages: | str. 365-395 |
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| Numbering: | Vol. 28, no. 3 |
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| PID: | 20.500.12556/RUP-1311  |
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| ISSN: | 0925-9899 |
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| UDC: | 519.17 |
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| COBISS.SI-ID: | 14625113 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 6706 |
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| Downloads: | 144 |
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| Metadata: |    |
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