FAKTORISASI PADA GRAF REGULER

Authors

  • Joko Prasetio Universitas Muhammadiyah Ponorogo
  • Arta Ekayanti Universitas Muhammadiyah Ponorogo

DOI:

https://doi.org/10.24269/ed.v4i1.434

Abstract

This research aims to: (1) know the criteria of a graph that has a -factor, (2) know the conditions of a regular graph that has a 1-factorization , (3) know the conditions of a regular graph that has a 2-factorization.

This research is a qualitative descriptive study using the method of literature study or literature review where a study of books, scientific journals, and other literature languages is carried out relating to factorization on regular graphs. This research begins by discussing the definitions and examples of euler graphs and regular bipartite multigraphs. Next in reviewing the terms of a regular graph which has a 1-factorization and which has a 2-factorization, it starts by discussing the definition and theorem of matching on bipartite graphs, definitions and examples of factorization graphs, then discussing the proof of theorem of regular graphs that have a 1-factor and a regular graph which has a 2-factor.

The results of this study indicate that: (1) Graph  is said to be -factorable  or can be factored into -factor , if can be decomposed or be eksplained into spanning subgraphs , where each  has a -factor and is edge-disjoint from , that is 1)  2)  … n) = . (2) The condition for a graph that has a 1-factorization is, if the graph is a -regular bipartite multigraph, with . (3) The condition for a graph that has a 2-factorization is, if the graph is a -regular graph, with .

               

Key words: Bipartite graphs, Factorization, Decomposition, Regular graph.

References

Akiyama, J. dan Kano, M. 2007. Factors and Factorizations of Graph. Diambil pada tanggal 13 maret 2019, dari http://gorogoro.cis.ibaraki.ac.jp/web/papers/FactorGraphVer1A4.pdf.

Chartrand, G. dan Leniak, L. 2000. Graphs & Digraphs (3th ed). California: Chapman and Hall.

Chartrand, G. dan Leniak, L. 1986. Graphs & Digraphs . California: a Division of Wadsworth, Inc.

Hasanah, S. 2008. Digraf dari Tabel Cayley Grup Dihedral. Skripsi tidak diterbitkan. Malang: Program Sarjana UIN Malang.

James, Robert C. 1992. Mathematics Dictionary. New York: Chapman and Hall.

Kerami, D. dan Sitanggang, C. 2003. Kamus Matematika. Jakarta: Balai Pustaka.

Munir, R. 2014. Matematika Diskrit. Bandung: Informatika Bandung.

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Published

2020-04-18

How to Cite

Prasetio, J., & Ekayanti, A. (2020). FAKTORISASI PADA GRAF REGULER. EDUPEDIA, 4(1), 75–92. https://doi.org/10.24269/ed.v4i1.434

Issue

Vol. 4 No. 1 (2020): April

Section

Articles

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