Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order

Abstract

We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.

Keywords

mathematics;graph theory;Cayley graph;abelian group;automorphism group;asymptotic;▫$p$▫-group;

Data

Language:	English
Year of publishing:	2010
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	519.17:512.54
COBISS:	15870041
ISSN:	1855-3966
Parent publication:	Ars mathematica contemporanea
Views:	4472
Downloads:	137
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Type (COBISS):	Not categorized
Pages:	str. 201-214
Volume:	ǂVol. ǂ3
Issue:	ǂno. ǂ2
Chronology:	2010
ID:	1475398