Pelabelan Super Graceful pada Graf Caterpillar

Authors

  • 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

DOI:

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

Keywords:

Pelabelan Super Graceful, Graf Caterpillar.

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.

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.

Downloads

Published

2015-04-28

How to Cite

Nur Arafah, N., Ramdani, R., & Fatchul Huda, A. (2015). Pelabelan Super Graceful pada Graf Caterpillar. KUBIK: Jurnal Publikasi Ilmiah Matematika, 1(1), 38–48. https://doi.org/10.15575/kubik.v1i1.322

Issue

Vol. 1 No. 1 (2015): KUBIK : Jurnal Publikasi Ilmiah Matematika

Section

Articles

Citation Check

License

Authors who publish in KUBIK: Jurnal Publikasi Ilmiah Matematika agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

 

 

Similar Articles

You may also start an advanced similarity search for this article.