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1、GRAPHS,GROUPSANDSURFACESNORTH-HOLLANDMATHEMATICSSTUDIES8NORTH-HOLLAND-AMSTERDAMNEWYORKOXFORDGRAPHS,GROUPSANDSURFACESArthurT.WHITEWesternMichiganUniversityKalamazoo,MichiganU.S.A.Completelyrevisedandenlargededition1984NORTH-HOLLAND-AMSTERDAM0NEWYORKOXFORDElsevierSciencePublishers
2、E.V.,1984Allrightsreserved.Nopartofthispublicationmaybereproduced,staredinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutthepriorpermissionofthecopyrightowner.Firstedition:Firstprinting1973Revisededition:Firstp
3、rinting1984ISBN:044487643xPublishers:ELSEVIERSCIENCEPUBLISHERSB.V.P.O.BOX19911000EZAMSTERDAMTHENETHERLANDSSoledistributorsfortheU.S.A.andCanada:ELSEVIERSCIENCEPUBLISHINGCOMPANY,INC.52VANDERBILTAVENUENEWYORK,N.Y.10017U.S.A.LibraryofCongressCataloginginPubllcationDataWhite,ArthurT
4、.Graphs,groups,andsurfaces.(North-Hollandlllathematicsstudies;8)Bibliography:p.Includesindexes.1.Graphtheory.2.Groups,Theoryof.3.Combina-torialtopolo.I.Title.11.Series.W66.W4519%511'.584-18853ISBN0-444-87643-XPRINTEDINTHENETHERLANDSVFOREWORDTOTHEFIRSTEDITIONThistextisbasedonacou
5、rsethatItaughtatWesternMichiganUniversityin1971.Thematerialissuitableforpresentationatthegraduateoradvancedundergraduatelevel,andassumesonlyanintro-ductoryknowledgeofgrouptheoryandofpoint-settopology.Oneofthefeaturesofthesubjectmatteristhatmanyresultsofthegeneraltheorycanbereadi
6、lyvisualized,ormodeled,sothatthestudentisconstantlyreassuredthatwhatheisdoinghasmeaning,ismorethanaformalmanipulationofsymbols.Thefocusofattentionisaninteractionamounggraphs,groups,andsurfaces(seeFigure0-1).Afterabriefintroductiontothetheoryofgraphs,therelationshipbetweengraphsa
7、ndgroupswillbeexplored.Foreverygraphthereisanassociatedgroup,calledtheautomorphismgroupofthegraph.Conversely,foreverygrouppresen-tation,thereisanassociatedgraph,calledaCayleycolorgraphofthegroup.Bothassociationswillbestudied,withemphasisonthelatter.Anexcursionintocombinatorialto
8、pologywillfollow;Euler'sgeneralizedpolyhedralfo
