| Title: | Semiregular automorphisms of vertex-transitive graphs of certain valencies |
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| Authors: | ID Dobson, Edward (Author)
ID Malnič, Aleksander (Author)
ID Marušič, Dragan (Author)
ID Nowitz, Lewis A. (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.jctb.2006.06.004
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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: | It is shown that a vertex-transitive graph of valency ▫$p+1$▫, ▫$p$▫ a prime, admitting a transitive action of a ▫$\{2,p\}$▫-group, has a non-identity semiregular automorphism. As a consequence, it is proved that a quartic vertex-transitive graph has a non-identity semiregular automorphism, thus giving a partial affirmative answer to the conjecture that all vertex-transitive graphs have such an automorphism and, more generally, that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs, Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997) 605-615]). |
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| Keywords: | mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph |
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| Year of publishing: | 2007 |
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| Number of pages: | str. 371-380 |
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| Numbering: | Vol. 97, iss. 3 |
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| PID: | 20.500.12556/RUP-7722  |
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| ISSN: | 0095-8956 |
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| UDC: | 519.17:512.54 |
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| COBISS.SI-ID: | 14287961 |
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| Publication date in RUP: | 03.04.2017 |
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| Views: | 2462 |
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| Downloads: | 83 |
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