Distance-transitive graphs admit semiregular automorphisms

Klavdija Kutnar (Author), Primož Šparl (Author)

Abstract

A distance-transitive graph is a graph in which for every two ordered pairs ofvertices ▫$(u,v)$▫ and ▫$(u',v')$▫ such that the distance between ▫$u$▫ and ▫$v$▫ is equal to the distance between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫ and ▫$v$▫ to ▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of equal length in its cycle decomposition. It is shown that every distance-transitive graph admits a semiregular automorphism.

Keywords

distance-transitive graph;vertex-transitive graph;semiregular automorphism;permutation group;

Data

Language:	English
Year of publishing:	2010
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.17
COBISS:	1024085332
ISSN:	0195-6698
Views:	3220
Downloads:	98
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Type (COBISS):	Not categorized
Pages:	str. 25-28
Volume:	ǂVol. ǂ31
Issue:	ǂno. ǂ1
Chronology:	2010
DOI:	10.1016/j.ejc.2009.03.018
ID:	1477156