1、密級——若干圖類的虧格分布研究StudyofGenusDistributionsForSomeGraphs博士生姓名：。絲塑—鹽指導教師姓名、職稱學科專業(yè)研究方向黃元秋教授運籌學與控制魚圖論及其應(yīng)甩湖南師范大學學位評定委員會辦公室二零一陸年三月ABSTRACTThegenusdistributionwasfirstlyintroducedbyGrossandFurstin【101，asoneofimportanttopologicali

2、nvariantsofgraphsItentirelydescribethatthedistributionofthenumberoftheallembeddings，whichOnthegivenandorientablesurfacesthatthegraphcaJlbeembededintoItstheoryhasbeenappliedinjudgmentinggraphisomorphism，calculatingofcompl

3、exalgebraiccurvemodespace，quantumfieldtheoryandstringtheoryoftheoreticalphysicsandSOonSincethelastcenturymanyfamousscholarsathomeandabroadintheresearchofthisfieldForexample：White，Gross，Mohar，Stahl，Tucker，Bonnington，F(xiàn)urst

4、，TesaranddomesticProfessorLiuYanpei，andSOonHowever，Thomassenhasbeenproventhatcalculatingthegenusdistributionsofthegeneral寥aphsisNPeompleteBecauseofitsdifficultytheresultsofthegenusdistributionsofthegraphsaren’tveryrich，a

5、ndtheclassesofgraphswhosethegenusdistributioncanbedeterminedhavespecialstructures，whichmakesthatmanyofmethodscan’tbegeneralizedtogeneralgrapllsInthispaper，wetrytoapplysomenewmethodstoexplorethegenusdistributionsofsomegra

6、phclassesseveralresultsaxederivedasfollows：1Let(G，u，V)beadoublerootedgraphwithtwo2valentcoroots“andVIn2011，Grossstudiedthegenusdistributionofthegrapheomformedbyselfpastingatrootverticesofthegraph(G，讓，V)inliterature【15]In

7、thesecondchapterofthispaper，thegenusdistributionofadoublerootedgraphwhoseoneroothasarbitrarydegreeafterselfpastingatrootverticeshavebeenderived，byappl妒ngvertexdeleting，edgeaclditiontheorem，multipleproductionrulesandselfa

8、malgamationtheorem；Andanalogousresultsof“t—WOrootsaretwodegree”inliterature[15]hadbeenprovidedbyGrosshavebeengeneralized2D3RisthecartesianproductofadipolegraphDaandapathRWederivearecursionforthegenusdistributionofthegrap

9、hD3Pn，withtheaidofskillfullyintroducinganewkindofedgesaddingoperationsandcombiningthepartialgenusdistributionofthegraph3Calculatingthegenusdistributionsofouterplanargraphsisacon—cernedtopicintopologicalgraphtheoryInthefo