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INVOLUTION GRAPHS WHERE THE PRODUCT OF TWO ADJACENT VERTICES HAS ORDER THREE

Part of: Permutation groups Graph theory

Published online by Cambridge University Press:  01 December 2008

ALICE DEVILLERS  and
MICHAEL GIUDICI
ALICE DEVILLERS
Affiliation:
Université Libre de Bruxelles, Département de Mathématiques, Géométrie – CP 216, Boulevard du Triomphe, B-1050 Bruxelles, Belgium (email: adevil@ulb.ac.be)
MICHAEL GIUDICI*
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia (email: giudici@maths.uwa.edu.au)
*
✉For correspondence; e-mail: giudici@maths.uwa.edu.au
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Abstract

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An S3-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G=PSL(2,q).

Keywords

graphsgroupsinvolutions

MSC classification

Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 305 - 322
Copyright
Copyright © Australian Mathematical Society 2009

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