全圖補(bǔ)圖的哈密爾頓性.pdf

1、Y900389碩士吾j4完蘭‘學(xué)位論文新疆大學(xué)論文題目(中文)：全圖補(bǔ)圖的哈密爾頓性論。芝題目(外文)：HamiltonicltyefComplementsofTotalGrapls研究生姓名：馬國(guó)燕學(xué)科專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：囤論及乒應(yīng)用導(dǎo)師舛名職稱：吳寶音都仍教授論文答辯日期年月日學(xué)位授予日期年月日AbstractForagraphG，thetotalgraphT(G)ofGisthegraphwithvertexsetv(a)UE

2、(G)inwhichthevertices。andYarejoinedbyanedgeifxandYareadjacentorincidentinGLetGbethecomplementsoftotalgraphsT(G)Inthisthesis，weconcentrateonthehamiltonicityofthecomplementsoftotalgraphsT(G)ofsimplegraphsGWuBaoyindurengand

3、MengJixiangin(Basicpropertiesoftotaltransformationgraphs，JMathStudy34(2)(2001)109116)establishedsomebasicpropertiesofGforagraphGTheyprovedthatGisconnectedifandonlyifGisneitherastarnoratriangleTheyalsoprovethatifGisneithe

4、rastarnoratriangle，thendiam(G)≤3HararyandNash—Williamsin(Oneulerianandhamiltoniangraphsandlinegraphs，CanadMathBull8(1965)701—709)provedthatL(G)ishamiltonianifandonlyifGhasaclosedtrailin—cidentwitheachedgeWecallthecomplem

5、entoflinegraphofagraphG，thejumpgraphofGadoptingthenotionin(Subgraphdistancesingraphsdefinedbyedgetransfers，DiscreteMath170(1997)6379)WuandMengin(Hamiltonianjumpgraphs，DiscreteMath289(2004)95106)giveasimplesufficientandne

6、cessaryconditionforagraphGwhoseJ(G)ishanfiltonianMotivatedfromtheresultsabove，weprovethatK(G)≥6(a)一landfurtherestablishthatG——————ishamiltonianifandonlyifGisnotisomorphictoanygraphinKl，一r≥1)uK1，。尬Is≥1U／t“1，telt≥2)u瑪，K3Ⅳ1