Rainbow Antimagic Coloring pada Graf Hasil Operasi Comb Graf Lintasan
Keywords:
pelabelasan antimagic, graf lintasan, pewarnaan pelangiAbstract
Misalkan ???? adalah graf terhubung dengan himpunan titik ????(????) dan himpunan sisi ????(????). Misalkan fungsi ????: ????(????) ? {1,2,3, … , |????(????)|} adalah fungsi bijektif. Bobot sisi dari graf ???? didefinisikan sebagai ????(????????) = ????(????) + ????(????). Jika terdapat lintasan ???? ? ???? dengan setiap dua sisi ????????, ????’????’ ? (????) pada lintasan ???? ? ???? mempunyai bobot yang berbeda yaitu, ????(????????) ? ????(??????????) maka fungsi bijektif ???? disebut rainbow antimagic labeling. Dengan demikian jika dipandang bobot sisi ????(????????) sebagai pewarnaan sisi ????????, maka ???? juga disebut rainbow antimagic coloring. Rainbow antimagic connection number adalah jumlah warna paling kecil dari semua rainbow antimagic coloring pada graf ????, dinotasikan dengan ????????????(????). Pada makalah ini, dipelajari tentang rainbow antimagic coloring dan diperoleh nilai dari rainbow antimagic connection number pada graf hasil operasi comb pada graf lintasan ????7 ? ????4 dan ????7 ? ????6.
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