半群Cayley圖的若干研究.pdf

1、蘭州大學(xué)博士學(xué)位論文半群Cayley圖的若干研究姓名：郝怡非申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：數(shù)學(xué)、基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：羅彥鋒20100501蘭州大學(xué)2010屆博士學(xué)位論文AbstractThisdissertationconsistsoffivechaptersWestudythepropertiesandconstructionsoftheCayleygraphsofsomesemigroupsInthefirstchapter，theCayl

2、eygraphsofBrandtsemigroupswillbeinvestigatedThebasicstructuresandpropertiesofthiskindofCayleygraphsaregiven，andanecessaryandsufficientconditionisgivenforthecomponentsofCayleygraphsofBrandtsemigroupstobestronglyregularAsa

3、napplication，thegeneralizedPetersengraphandkpartitegraph，whichcannotbeobtainedfromtheCayleygraphsofgroups，canbeconstructedasacomponentoftheCayleygraphsofBrandtsemigroupsInChapter2，theCayleygraphsofcompletelysimplesemigro

4、upswillbeinvesti—gatedThebasicstructureandpropertiesofthiskindofCayleygrapharegivenandaconditionisgivenforaCayleygraphofacompletelysimplesemigrouptobeadisjointunionofcompletegraphsWealsodescribeallthecompletelysimplesemi

5、groupswithstronglyconnectedbipartiteCayleygraphsInChapter3，theCayleygraphsoftheleftgroupsandoftherightgroupsareinvestigated，respectivelyThebasicstructuresandpropertiesofthesetwokindsofCayleygraphsaregivenWeprovethattheun

6、directedCayleygraphsoftherightgroupsareisomorphictotheCayleygraphsofgroupGZnwithrespecttoappropriateconnectionsetsAsanapplication，wegivethestructureoftheundirectedCayleygraphsoftherectangulargroupsInparticular，wegiveacom

7、pletedescriptionofvertextransitiveCayleygraphsofthestrongsemilatticeofrectangulargroupsInChapter4，let取bethesymmetricinversesemigrouponafinitenonemptysetx，Abeasubsetof致(取＼o))WeobtainaconditionofCay(Z支，A)(whichisobtainedby

8、deletingvertex0fromtheCayleygraphof取withrespecttoA)tobeColAutA(瓦)一vertextransitiveandAUtA(2支：)一vertextransitive，respectivelyThebasicstructureofvertextransitiveCay(Z支，A)ischaracterizedWealsoprovethatthegeneralizedPetersen