Pelabelan Super Graceful pada Graf Caterpillar

Nisa Nur Arafah; Rismawati Ramdani; Arief Fatchul Huda

doi:10.15575/kubik.v1i1.322

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Nisa Nur Arafah
UIN Sunan Gunung Djati Bandung
Indonesia

Rismawati Ramdani
UIN Sunan Gunung Djati Bandung
Indonesia

Arief Fatchul Huda
UIN Sunan Gunung Djati Bandung
Indonesia

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Pelabelan Super Graceful pada Graf Caterpillar

Nisa Nur Arafah^(1*), Rismawati Ramdani⁽²⁾, Arief Fatchul Huda⁽³⁾

(1) UIN Sunan Gunung Djati Bandung, Indonesia
(2) UIN Sunan Gunung Djati Bandung, Indonesia
(3) UIN Sunan Gunung Djati Bandung, Indonesia
(*) Corresponding Author

Abstract

Misalkan G merupakan suatugraf dengan banyaknya titik pdan banyaknya sisi q. Pelabelan super graceful adalah pemetaan fungsi satu-satu pada f ∶ V(G) ∪ E(G) → {1,2, ... , p + q}sehingga f(uv) = |f(u) − f(v)| berbeda untuk setiap sisi uv ∈ E(G). Sebuah graf G disebut graf super graceful jika graf tersebut dapat dilabeli menurut definisi pelabelan super graceful. Graf caterpillar adalah graf yang jika semua titik pendannya dihilangkan akan menghasilkan lintasan. Pada makalah ini akan ditunjukkan bahwa graf caterpillar Cp n dengan kepala dan ekor yang mempunyai n badan dan 2 kaki pada tiap badan, graf caterpillar Cp n tanpa kepala dan ekor yang mempunyai n badan dan 2 kaki pada tiap badan,dan graf caterpillar Cp m,n tanpa kepala dan ekor yang mempunyai n badan dan m kaki pada tiap badan merupakan graf super graceful.

Keywords

Pelabelan Super Graceful, Graf Caterpillar.

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References

Bala, E, dkk, Graph labeling in competition graph, Indian Journal of Science and Technology, 4(8): 0974-6846, 2011.

Fathoni, A, Pelabelan Super Sisi Ajaib padaGraph Caterpillar, Tugas Akhir, Jurusan Matematika Fakultas Sains dan Teknologi, Universitas Islam Negeri Malang, 2009.

Gallian, J.A, A Dynamic Survey of Graph Labeling, tenth edition, The Electronic Journal of Combinatorics, 17(11): 05C78, 2011.

J.A. BondydanMurty, Graph Theory with Applications, Penerbit The Macmillan Press Ltd, 1976.

Kusumah, Y.S, Matematika Diskrit, Penerbit IKIP Bandung Press, 1997.

Munir, R, Matematika Diskrit, Penerbit Informatika, 2005.

Perumal, M.A., dkk, Super Graceful Labeling For Some Special Graphs, Journal Mathematics, 9(3): 06, 2011.

Watson, R. Lynn, A Survey on The Graceful Labeling of Graph, This Thesis for the Master of Science, University of Colorado at Denver in Partial fulfillment of the requirements for the degree of Master of Science Applied Mathematics, 2000.

DOI: https://doi.org/10.15575/kubik.v1i1.322

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Pelabelan Super Graceful pada Graf Caterpillar

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