Semiregular automorphisms of vertex-transitive graphs of certain valencies

Dobson, Edward; Malnič, Aleksander; Marušič, Dragan; Nowitz, Lewis A.

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Title:	Semiregular automorphisms of vertex-transitive graphs of certain valencies
Authors:	ID Dobson, Edward (Author) ID Malnič, Aleksander (Author) ID Marušič, Dragan (Author) ID Nowitz, Lewis A. (Author)
Files:	http://dx.doi.org/10.1016/j.jctb.2006.06.004
Language:	English
Work type:	Not categorized
Typology:	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
PID:	20.500.12556/RUP-7722
ISSN:	0095-8956
UDC:	519.17:512.54
COBISS.SI-ID:	14287961
Publication date in RUP:	03.04.2017
Views:	3204
Downloads:	90
Metadata:
:	DOBSON, Edward, MALNIČ, Aleksander, MARUŠIČ, Dragan and NOWITZ, Lewis A., 2007, Semiregular automorphisms of vertex-transitive graphs of certain valencies. [online]. 2007. Vol. 97, no. 3, p. 371–380. [Accessed 14 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.jctb.2006.06.004 Copy citation

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Secondary language

Language:	English
Keywords:	matematika, teorija grafov, tranzitivna permutacijska grupa, 2-zaprta grupa, polregularni avtomorfizem, točkovno tranzitivni grafi

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