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1、CAMBRIDGETRACTSINMATHEMATICSGENERALEDITORSH.BASS,J.F.C.KINGMAN,F.SMITHIESJ.A.TODD&C.T.C.WALL67.AlgebraicgraphtheoryNORMANBIGGSLecturerinMathematicsMoyalHollowayCollege,UniversityofLondonAlgebraicGraphTheoryCAMBRIDGEUNIVERSITYPRESSPublishedbytheSyndics
2、oftheCambridgeUniversityPressBentleyHouse,200EustonRoad,LondonNW12DBAmericanBranch:32East57thStreet,NewYork,K.Y.10022(g)CambridgeUniversityPress1974LibraryofCongressCatalogueCardNumber:73-86042ISBN:052120335XFirstpublished1974PrintedinGreatBritainatth
3、eUniversityPrintingHouse,Cambridge(BrookeCrutchley,UniversityPrinter)ContentsPrefacepagevii1Introduction1PARTONE-LINEARALGEBRAINGRAPHTHEORY2Thespectrumofagraph93Regulargraphsandlinegraphs144Thehomologyofgraphs225Spanningtreesandassociatedstructures296
4、Complexity347Determinantexpansions40PARTTWO-COLOURINGPROBLEMS8Vertex-colouringsandthespectrum499Thechromaticpolynomial5710Edge-subgraphexpansions6411Thelogarithmictransformation7212Thevertex-subgraphexpansion7813TheTuttepolynomial8614Thechromaticpolyn
5、omialandspanningtrees94PARTTHREE-SYMMETRYANDREGULARITYOFGRAPHS15Generalpropertiesofgraphautomorphisms10116Vertex-transitivegraphs10617Symmetricgraphs112viContents18Trivalentsymmetricgraphspage11919Thecovering-graphconstruction12720Distance-transitiveg
6、raphs13221Thefeasibilityofintersectionarrays14022Primitivityandimprimitivity14723Minimalregulargraphswithgivengirth154Bibliography165Index169PrefaceItisapleasureformetoacknowledgethehelpwhichIhavereceivedduringthepreparationofthisbook.Apreliminarydraf
7、tofthemanuscriptwasreadbyDrR.J.Wilson,andhisdetailedcommentsresultedinsubstantialchangesandimprove•ments.Iwasthenfortunatetobeabletorelyupontheexpertassistanceofmywifefortheproductionofatypescript.Ideasandhelpfulcriticismswereofferedbyseveralfriendsan
8、dcol•leagues,amongthemG.deBarra,R.M.Damerell,A.D.Gardiner,R.K.Guy,P.McMullenandJ.W.Moon.ThegeneraleditoroftheCambridgeMathematicalTracts,ProfessorC.T.C.Wall,wasswiftandperceptiveinhisappraisal,andhiscom•mentsweremuchappreciated.ThestaffoftheCa
