17161.給定懸掛點(diǎn)數(shù)的單圈圖的極值斜能量

1、學(xué)校代碼!Q墨絲密級(jí)給定懸掛點(diǎn)數(shù)的單圈圖的極值斜能量OnExtremalSkewEnergyofUnicyclicGraphswithGivenPendent昵rtices研究生姓名：毛慧指導(dǎo)教師姓名、職稱：侯耀平教授學(xué)科專業(yè)：運(yùn)籌學(xué)與控制論研究方向：圖論及其應(yīng)用湖南師范大學(xué)學(xué)位評(píng)定委員會(huì)辦公室二零一五年四月ABSTRACTGraphtheoryisanimportantbranchofcombinatorialmathematicsI

2、thasawiderangeofimportantapplicationinfieldssuchaScomputer，chemical，physicsLetGbeasimplegraphTheenergyofthegraphE(G1isdefinedasthesumoftheabsolutevalueofalltheeigenvaluesoftheadjacencymatrixA(G)Inrecentyears：withthedevel

3、opmentofgraphenergNmanyscholarsbegintopayattentiontostudytheenergyofothermatricessuchastheLaplacianmatrixincidencematrixandthedistancematrixLetGbeanorientedgraphofgraphG，theskewenergy忍(G)oftheorientedgraphsGisdefinedasth

4、esumofthenormsofalltheeigenvaluesoftheskewadjacencymatrixS(G)Inthestudyofgraphenergyandtheskewenergy，extremeenergyproblemwithgraphicparametershaSbeenahotresearchproblemingraphtheoryThisthesismainlystudiestheskewenergyext

5、remalproblemofuni—cyclicgraphswiththegivenpendentverticesLeta(n，忌)bethegivenpendentverticesofunicyclicgraphstemoveQ黔LetO(n，，k)beaunicycliegraphclassofC(n，k)withprescribedgirthThemainresultofthisthesisarefollowing：(1)show

6、that一磁‘(3Sj≤n一七一1)istheminimumskewenergyoftheorientedunicyclicgraphamongtheunicyclicgraphclassofG(n，1；k)(3≤f≤n—k一1)withprescribedgirth，一磁^istheminimumskewenergyamongtheunicyclicgraphclassof、一磁2(3s1≤n一是一1)Namely，一磁‘isthem

7、inimumskewenergyofamongtheunicyclicgraphclassofG(n，南)(2)showthatQ≯istheminimumskewenergyoftheorientedunicycliegraphamongtheunicyclicgraphclassofQ2(3≤l≤佗一七一1)Keywords：unicycliegraph；skewenergy；orientedgraph；extremalprob一1