13469.有向圖mcn的優(yōu)美性和廣義petersen圖的(a,d)反邊幻標(biāo)號的研究

1、分類號——ICS學(xué)校代碼!Q13魚學(xué)號2Q!幽姜l￡～菱一3復(fù)內(nèi)蒙古民撤大學(xué)碩士學(xué)位論文有向圖朋t的優(yōu)美性和廣義Petersen圖的(口，d)一反邊幻標(biāo)號的研究StudyOntheGracefulnessoftheDigraph肌tandthe(口，d)一AntimagicLabelingsoftheGeneraIizedPetersenGraph申請人：包晶晶學(xué)科專業(yè)：應(yīng)用數(shù)學(xué)研究方向：圖論及其應(yīng)用學(xué)位類別：學(xué)術(shù)學(xué)位指導(dǎo)教師：吉日木圖

2、教授論文提交日期：二O一六年六月OntheGracefuInessoftheDigraphmtandthe(口，d)一AntimagicLabelingsoftheGeneraI娩edPetersenGraphAbstractGr印htlleo巧lsabranchofmat|lematlcs，eSpeclallyanmlportantbmnchofdlscretemamIthasbeenappliedmmanydi膿rcntfields

3、mthefnodemworld，such懿physics，chemistⅨ硒tronomygeography，bi0Iogy，especiallywdelyused洫computerscenceThepapermailllystudiesthelabelofgraphTheproblemsofthegrace向hessIabelingofdigraph鋤d(a，d)觚tirIlagiclabelingofthegeneralizedPe

4、tersengrapharcStudiedbycomb證iIlgcomputerwithmemethodofmat|leImticalThemainworkisasfollo、vS：Pro佗ssorMapr叩ossedaco嗎ecturenlatnledi卿hm己isgracemlgraphifll991AndthepaperproVedthattIledigraph4tisagracemlgraph，wheren≥3MirkaMill

5、erandMartinBacaproposedaco嗎ecturethatthegeneralizedPetersengraphs跗，七)hasf三字，31一antimagiclabeling，when玎量o(mod2)，玎62≤七≤詈_1I＼Z，2pr。VedtIlatthegeneralizedPetersengraphP(療’7)has(塑筍，3)一antifIlagiclabeling，where，，≥16Thepaperuse

6、dtllismethodt0fmdt11egeneralizedPetersengraphP(”，9)，尸(圩，11)，尸(行，13)，尸(刀，15)hasf皇≠，31一antimagiclabel洫g，where玎≥2七2Then＼二／proVetheconjectureofMirl(aMillerandMarrtmBacaisreasomble，thatis，thegeneral砌PeterSen聊hS砌，七)has(三竽’3)一a

7、ntmgiclabelingwaLseS詛bliShed，wherenisevenKeyword：Digraph小己；Grace如llabeIing；GeneralizedPetersen目aph；(a，d)一antirnagiclabelingDirectedby：profJirimutu(PhD)AppIicantforMasterde蓉ree：BaoJingjing(AppIiedM甜l啪a6cs)【CouegeofMalh鋤at