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Title:Semiregular automorphisms of vertex-transitive graphs of certain valencies
Authors:Marušič, Dragan (Author)
Dobson, Edward (Author)
Malnič, Aleksander (Author)
Nowitz, Lewis A. (Author)
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
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]).
Keywords:mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Year of publishing:2007
Number of pages:str. 371-380
Numbering:Vol. 97, iss. 3
COBISS_ID:14287961 Link is opened in a new window
Categories:Document is not linked to any category.
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Keywords:matematika, teorija grafov, tranzitivna permutacijska grupa, 2-zaprta grupa, polregularni avtomorfizem, točkovno tranzitivni grafi


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