ALGORITHM FOR CONSTRUCTING TRIPLE IDENTITY GRAPH OF RING Z_n USING PYTHON

  • Vika Yugi Kurniawan Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0001-8475-7243
  • Chessa Fanny Ekasiwi Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, Indonesia
DOI: https://doi.org/10.30598/barekengvol18iss3pp1629-1638
Keywords: Commutative Ring, Triple Identity Graph, Python, Integer Ring Modulo-n

Abstract

Let R be a commutative ring. The triple identity graph of ring R is denoted by TE(R) with sets of vertices  Two different vertices  and  are adjacent if and only if there is an element  in  such that  and . To easily visualize the triple identity graph, a program is needed to represent it briefly. Python can easily manipulate, analyze, and visualize data. Therefore, this study uses Python to construct the algorithm for  In this research, some examples will be given and then be observed for new characteristics of the triple identity graph of ring  such as the connectedness, the diameter, and the girth. And we find the characterize  for which graph  is empty, connected, or Hamiltonian.

Downloads

Download data is not yet available.

References

I. Beck, “Coloring of commutative rings,” J. Algebr., vol. 116, no. 1, pp. 208–226, 1988, doi: 10.1016/0021-8693(88)90202-5.

D. F. Anderson, T. Asir, A. Badawi, and T. T. Chelvam, Graphs from Rings. Springer International Publishing, 2021. doi: 10.1007/978-3-030-88410-9.

D. F. Anderson and P. S. Livingston, “The zero-divisor graph of a commutative ring,” J. Algebr., vol. 217, no. 2, pp. 434–447, Jul. 1999, doi: 10.1006/jabr.1998.7840.

D. F. Anderson and D. Weber, “The zero-divisor graph of a commutative ring without identity,” Int. Electron. J. Algebr., vol. 23, 2018, doi: 10.24330/ieja.373663.

A. Durić, S. Jevcrossed d signenić, P. Oblak, and N. Stopar, “The total zero-divisor graph of a commutative ring,” J. Algebr. its Appl., vol. 18, no. 10, 2019, doi: 10.1142/S0219498819501901.

G. Kalaimurugan, P. Vignesh, and T. Tamizh Chelvam, “On zero-divisor graphs of commutative rings without identity,” J. Algebr. its Appl., vol. 19, no. 12, 2020, doi: 10.1142/S0219498820502266.

S. Pirzada, M. Aijaz, and M. I. Bhat, “On zero divisor graphs of the rings Zn,” Afrika Mat., vol. 31, no. 3–4, 2020, doi: 10.1007/s13370-019-00755-3.

E. Yetk, “THE TRIPLE ZERO GRAPH OF A COMMUTATIVE RING,” Com mun.Fac.Sci.Univ.Ank.Ser, no. 2, pp. 653–663, 2021, doi: 10.31801/cfsuasm.

F. Smarandache and W. B. V. Kandasamy, “Groups as graphs,” 2009. [Online]. Available: https://digitalrepository.unm.edu/math_fsp

H. Q. Mohammad and N. H. Shuker, “Idempotent Divisor Graph of Commutative Ring,” Iraqi J. Sci., vol. 63, no. 2, 2022, doi: 10.24996/ijs.2022.63.2.21.

V. Yugi Kurniawan, B. Purboutomo, and N. Arfawi Kurdhi, “Connectivity of The Triple Idempotent Graph of Ring Z n,” 2024.

V. K. Sharma, V. Kumar, S. Sharma, and S. Pathak, “Introduction to Python Programming,” in Python Programming, Chapman and Hall/CRC, 2021, pp. 1–8. doi: 10.1201/9781003185505-1.

T. Hartati and V. Y. Kurniawan, “Construct the triple nilpotent graph of ring using python,” in AIP Conference Proceedings, 2023. doi: 10.1063/5.0154928.

P. Wulandari, V. Y. Kurniawan, and N. A. Kurdhi, “CONSTRUCT THE TRIPLE ZERO GRAPH OF RING Z_n USING PYTHON,” BAREKENG J. Ilmu Mat. dan Terap., vol. 18, no. 1, 2024, doi: 10.30598/barekengvol18iss1pp0507-0516.

R. Meinawati, V. Y. Kurniawan, and N. A. Kurdhi, “Algorithm for Constructing Total Graph of Commutative Ring,” JTAM (Jurnal Teor. dan Apl. Mat., vol. 8, no. 2, p. 351, Mar. 2024, doi: 10.31764/jtam.v8i2.19850.

G. Chartrand, Introductory graph theory. New York: Dover Books, 1985.

S. Skiena, Implementing Discrete Mathematics. Redwood City, Calif: Addison Wesley Publishing Company, 1990.

J. P. Mazorodze and S. Mukwembi, “Radius, Diameter and the Degree Sequence of a Graph,” Math. Slovaca, vol. 65, no. 6, 2015, doi: 10.1515/ms-2015-0084.

G. Chartrand, H. Jordon, V. Vatter, and P. Zhang, Graphs & Digraphs. 2023. doi: 10.1201/9781003461289.

Published
2024-07-31
How to Cite
[1]
V. Kurniawan and C. Ekasiwi, “ALGORITHM FOR CONSTRUCTING TRIPLE IDENTITY GRAPH OF RING Z_n USING PYTHON”, BAREKENG: J. Math. & App., vol. 18, no. 3, pp. 1629-1638, Jul. 2024.
Issue
Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Vika Yugi Kurniawan, Chessa Fanny Ekasiwi

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Authors who publish with this Journal agree to the following terms:

  1. Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
  2. Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement 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 websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.