20803.單圈圖斜能量的排序

1、單圈圖斜能量的排序OrderingoftheOrientedUnicyclicGraphswithSkewEnergies研究生姓名：董情情指導教師姓名、職稱：侯耀平教授學科專業(yè)：運籌學與控制論研究方向：圖論及其應用湖南師范大學學位評定委員會辦公室二零一五年四月ABSTRACTThegraphtheoryisa，widelyusedmathematicaldiscipli麟Ith881m。Dortantapplicationsinthe

2、naturalscience，socialscienceandsoonRese缸cnkoutthetheoryofgraphspectraisanimportantfield跚daprettyactlve凈searchdirectioninthegraphtheoryIthasextremelywidespreadapplicati。o、nsintheresearchofqu鋤tumchemistryphysics，computersc

3、ienceandSoon’lesnectralgraphtheorymainlystudiestheeigenvalue—andeigenspaceSofPapslrvofthecorrelationmatrix(suchasadjacencymatrixandLaptacianmatrlXetc)TheenergyofagraphisapartofthespectralFaphth∞ryAn1mp叫一tantapplicationof

4、掣aphenergYinstructuralchemistryiS8sf01l。w&，Esp『!e『：ciallv’thereexistsaclosecorrespondencebetweeneigenvalueso‘graph：andthem—olecularorbitalenergYlevels。f7[electr。唑眥。njug眥dhydj：)咖∞瑚：Forasimpleundirectedgraph—G，theenergYE(刁

5、)isde缸edtobeeum毗theabs。lutevaluesof“eigeIⅣalues。fit8adjacen乞matriXIn1977th“a譬：mathematicchemistGutmanfirstpr。p。sedthetheoryofgraphene，rgywhlcnhasbeenev01vedintooneoftheveryaetivedirectionsongraphth：。eve：since。Moreover，it

6、haSbeenratherwidelyconeernedbytheoreticalchemlS‘andmathematiciaIlsParticularlysince2000，graphenergyhasbeendeeplydevelopedinwhichmanyimportantresultshavebeendiscove。edThisaspecthashadmanyconclusionsBesidesgraphenergyofthe

7、adjacencymatrix，afewotherrelate、dI弩1X。fthegraphenergyhavebeenproposedandwidelystudied，suchasL印1：c：篡ener既signlessLaplacianenergyincidenceenergY，dist眥呲mrgy一州‘：坨skew—energy。f。rientedgraphAnal。goust0thede6nitioIloft。he玄en。e。

8、!y：三simpleundirected鏟印h，theskewenergyofanofiented擎aphG1sdenedaSthesumoftheat)solutevaluesofalleigenvaluesofthecoHespondingskew—ad]acencymatrixUsingthemethodofcoefficientcomparionandthetheoremofzerop0IntsoffunctionWeinves