Pelabelan graceful kuadrat dan pelabelan graceful kuadrat genap pada graph (C3*3K1,n) dan graph (K1,n:m) / Retno Apriantika
| Main Author: | Apriantika, Retno |
|---|---|
| Format: | Thesis NonPeerReviewed |
| Terbitan: |
, 2017
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| Subjects: | |
| Online Access: |
http://repository.um.ac.id/17480/ |
Daftar Isi:
- ABSTRAKApriantikaRetno.2017.PelabelanGracefulKuadratdanPelabelanGracefulKuadratGenapPadaGraph9001C_3123103K12311_(1n)9002danGraph9001K_(1n)m9002.SkripsiJurusanMatematikaMIPAUniversitasNegeriMalang.PembimbingProf.Drs.PurwantoPh.D.KataKunciGraphPelabelanPelabelanGracefulKuadratPelabelanGracefulKuadratGenapGraph9001C_3123103K12311_(1n)9002Graph9001K_(1n)m9002.SuatugraphG(VE)denganbanyaknyasisiqdikatakangraphgracefulkuadratjikaadasuatufungsiinjektifdarihimpunantitikkehimpunan012q2sedemikiansehinggamenginduksipemetaanbijektifdarihimpunansisikehimpunan149q2dimanasisinyamendapatlabelhargamutlakdariselisihpelabelankeduatitikyangterhubunglangsung.Terdapatvariasibarudaripelabelangracefulkuadratyaitupelabelangracefulkuadratgenap.Padaskripsiiniditemukanhasilbaruyaitugraph9001C_3123103K12311_(1n)9002untukn88052adalahgraphgracefulkuadratdangraphgracefulkuadratgenap.Selainituakandibuktikangraph9001K_(1n)m9002dengandefinisipelabelantitikdansisiyangberbedadariliteraturadalahgraphgracefulkuadratsertaakandibuktikanbahwagraph9001K_(1n)m9002memenuhipelabelangracefulkuadratgenap.Pembuktiandilakukandengancaramenentukanfungsipelabelantitikkemudianmembuktikanfungsipelabelantitiknyainjektifdanfungsipelabelansisiyangdiinduksiolehfungsipelabelantitikadalahpemetaanbijektif.Daripembahasandiperolehbahwagraph9001C_3123103K12311_(1n)9002untukn88052dangraph9001K_(1n)m9002dapatdikenakanpelabelangracefulkuadratdanpelabelangracefulkuadratgenap.Pelabelangracefulkuadratdanpelabelangracefulkuadratgenapdikerjakandenganmelabelititikterlebihdahulukemudiandilanjutkandenganmelabelisisi.ABSTRACTApriantikaRetno.2017.SquareGracefulLabelingandEvenSquareGracefulLabelingonTheGraph9001C_3123103K12311_(1n)9002andGraph9001K_(1n)m9002.MinithesisDepartmentofMathematicsFacultyofMathematicandNaturalScienceStateUniversityofMalang.AdvisorsProf.Drs.PurwantoPh.D.KeywordsGraphLabelingSquareGracefulLabelingEvenSquareGracefulLabelingTheGraph9001C_3123103K12311_(1n)9002TheGraph9001K_(1n)m9002.AgraphG(VE)withqedgesissaidtobeasquaregracefulgraphifthereexistsaninjectionfunctionfromthesetofverticesto012q2suchthatinducedabijectionmappingfromthesetofedgesto149q2withtheedgelabelistheabsolutevalueofthedifferencebetweenthelabelingoftwoadjacentvertices.Thereisanewvariationofsquaregracefullabelingthatisanevensquaregracefullabeling.Inthisminithesishasfoundnewresultsthatthegraph9001C_3123103K12311_(1n)9002forn88052isasquaregracefulgraphandalsoanevensquaregracefulgraph.Inadditionherewillbeprovedthatthegraph9001K_(1n)m9002withthedefinitionofdifferentvertexandedgelabelingfunctionfromtheliteratureissquaregracefulgraphandherewillbeprovedthatthegraph9001K_(1n)m9002isanevensquaregracefullabeling.Theproofhasdonebydeterminingvertexlabelingfunctionandthenprovingthatthevertexlabelingsfunctionisaninjectionandprovingthattheedgelabelingsfunctionareinducedbyvertexlabelingsfunctionisabijectionmapping.Fromthediscussionitwasobtainedthegraph9001C_3123103K12311_(1n)9002forn88052andgraph9001K_(1n)m9002thatcanbeusedforsquaregracefullabelingandevensquaregracefullabeling.Thesquaregracefullabelingandevensquaregracefullabelingisdonebylabelingthevertexfirstandthenproceedwiththeedgelabel.