19751.pq階完全圖的齊次分解

1、Pq階完全圖的齊次分解Homogfactorisationsofthepletegeneousactorlsecomplete1一o一‘●gradno士orderaDroductottwodistinctDrlmeS碩士生姓名：趙凱莉指導(dǎo)教師姓名、職稱：孫少輝講師學(xué)科專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：有限置換群與組合結(jié)構(gòu)湖南師范大學(xué)學(xué)位評定委員會辦公室二零一五年五月ABSTRACTBefore，expertsstudiedcyclichomoge

2、neousfactorisationsofcompletegrapll8onthebasisofselfcomplementaryvertextransitiveFaphSthispaperfurtherdevelopstheisomorphicproblemofcyclichomogeneousfactorisationsofcomoplete驢印hstothis，astheanalysisofCaleygraphs’isomorph

3、ism，thepaperdefineCayleystaininggraph，andextendsAdAm’Sconjecture，andcomestoaconclusion，thatforthecompletegraphoforderaproductoftwodistinctprimes，Cay(，S，妒)竺Cay(，s7，妒7)，ifandonlyif，theree)(ists釷∈互品SOthat&=札≤(i=1，，尼)Atlast，

4、thepaperstructsthecyclichomogeneousfactorisationsof歷3，Z91，andachievesthecountofnonisomorphismofhomogeneousfactorisationsThefulltextisdividedinto3chapters，themaincontentisasfollowsThechapter1，introductresearchbackground；a

5、ndonthebasisofdefiningCayleystaininggraph，extendsomebasicconceptsandproperties，toprepareforthestudyofisormorphicproblemthechapter2，determinenecessaryandsufficientconditionoftwocyclichomogeneousfactorisations’isormorphism

6、ofcompletegraphoforderprime，andachievethecountsofnonisormorphismofcyclichomogeneousfactorisationsofZ13thechapter3，determinenecessaryandsufficientconditionoftwocyclichomogeneousfactorisations’isormorphismofcompletegraphof

7、orderaproductoftwodistinctprimes，andachievethecountsofnonisormorphismofcyclichomogeneousfactorisationsofZ91Keywords：homogeneousfactorisations，Cayleystaininggraph，AdAm’Sconjecture，thecountofnonisomorphismofhomogeneousfact