Topics in Graph Automorphisms and Reconstruction

209 Pages·2016·1.522 MB·English

by  Josef Lauri, Raffaele Scapellato

LONDONMATHEMATICALSOCIETYLECTURENOTESERIES
ManagingEditor:ProfessorM.Reid,MathematicsInstitute,
UniversityofWarwick,CoventryCV47AL,UnitedKingdom
Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat
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LondonMathematicalSocietyLectureNoteSeries:432
Topics in Graph Automorphisms
and Reconstruction
SecondEdition
JOSEF LAURI
UniversityofMalta
RAFFAELE SCAPELLATO
PolitecnicodiMilano
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(cid:2)c JosefLauriandRaffaeleScapellato2016
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Firstpublished2016
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Names:Lauri,Josef,1955–|Scapellato,Raffaele,1955–
Title:Topicsingraphautomorphismsandreconstruction/
JosefLauriandRaffaeleScapellato.
Description:2ndedition.|Cambridge:CambridgeUniversityPress,2016.|
Series:LondonMathematicalSocietylecturenoteseries;432|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016014849|ISBN9781316610442(pbk.:alk.paper)
Subjects:LCSH:Graphtheory.|Automorphisms.|Reconstruction(Graphtheory)
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Lil
MaryAnne,
Christina,BeppeuSandrina
A
Fiorella
LondonMathematicalSocietyLectureNoteSeries:432
Topics in Graph Automorphisms
and Reconstruction
JOSEF LAURI
UniversityofMalta
RAFFAELE SCAPELLATO
PolitecnicodiMilano

Contents
PrefacetotheSecondEdition pagexi
PrefacetotheFirstEdition xiii
1 GraphsandGroups:Preliminaries 1
1.1 Graphsanddigraphs 1
1.2 Groups 3
1.3 Graphsandgroups 7
1.4 Edge-automorphismsandline-graphs 10
1.5 Awordonissuesofcomputationalcomplexity 13
1.6 Exercises 15
1.7 Notesandguidetoreferences 17
2 VariousTypesofGraphSymmetry 18
2.1 Transitivity 18
2.2 Asymmetricgraphs 25
2.3 Graphsymmetriesandthespectrum 29
2.4 Simpleeigenvalues 31
2.5 Highersymmetryconditions 32
2.6 Exercises 35
2.7 Notesandguidetoreferences 38
3 CayleyGraphs 39
3.1 Cayleycolourgraphs 39
3.2 Frucht’sandBouwer’sTheorems 42
3.3 Cayleygraphsanddigraphs 44
3.4 TheDoyle-HoltGraph 47
3.5 Non-Cayleyvertex-transitivegraphs 48
3.6 CosetgraphsandSabidussi’sTheorem 49
3.7 Doublecosetgraphsandsemisymmetricgraphs 51
vii