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Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

LOCAL IRREGULARITY VERTEX COLORING OF BICYCLIC GRAPH FAMILIES

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  • Arika Indah Kristiana,
  • Aji Mansur Santoso,
  • Saddam Hussen,
  • Edy Wihardjo,
  • Robiatul Adawiyah,
  • Dafik Dafik
Arika Indah Kristiana
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
Aji Mansur Santoso
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
Saddam Hussen
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
Edy Wihardjo
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
Robiatul Adawiyah
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
Dafik Dafik
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss2pp1093-1108
Published April 1, 2025
Keywords
  • Bicyclic Graphs,
  • Local Irregularity,
  • Vertex Coloring
How to Cite
[1]
A. I. Kristiana, A. M. Santoso, S. Hussen, E. Wihardjo, R. Adawiyah, and D. Dafik, “LOCAL IRREGULARITY VERTEX COLORING OF BICYCLIC GRAPH FAMILIES”, BAREKENG: J. Math. & App., vol. 19, no. 2, pp. 1093-1108, Apr. 2025.

Copyright (c) 2025 Arika Indah Kristiana, Aji Mansur Santoso, Saddam Hussen, Edy Wihardjo, Robiatul Adawiyah, Dafik Dafik

Creative Commons License

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

Abstract

The graph in this research is a simple and connected graph with  as vertex set and  as an edge set. We used deductive axiomatic and pattern recognition method. Local irregularity vertex coloring is defined as mapping  as vertex irregular -labeling and  where . The conditions for  to be a local irregularity vertex coloring, if  with  as irregularity vertex labeling and for every . The minimum number of colors produced from local irregularity vertex coloring of graph  is called chromatic number local irregularity, denoted by . In this research, we analyze about the local irregularity vertex coloring and determine the chromatic number of local irregularity of bicyclic graphs.

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References

  1. G. Saputra et al., “ON THE LOCAL IRREGULARITY VERTEX COLORING OF PENCIL GRAPHS,” AXIOMA, vol. 9, no. 1, pp. 97–105, 2024.
  2. Slamin, TEORI GRAF DAN APLIKASINYA EDISI KEDUA. R12 Group, 2023. [Online]. Available: https://www.academia.edu/95939687/Teori_Graf_dan_Aplikasinya_Edisi_Kedua_Copyright_Slamin_216_halaman_16_x_23_cm_Hak_cipta_ada_pada_penulis
  3. I. H. Agustin, Dafik, Slamin, R. Adawiyah, and E. Y. Kurniawati, “ON THE STUDY OF LOCAL ANTIMAGIC VERTEX COLORING OF GRAPHS AND THEIR OPERATIONS,” ICCGANT 2020, 2021, doi: 10.1088/1742-6596/1836/1/012018.
  4. Slamin, TEORI GRAF DAN APLIKASINYA. CV. Dream Litera Buana, 2019. [Online]. Available: https://repository.unej.ac.id/jspui/bitstream/123456789/91043/1/F. IK_Buku_Slamin_Teori Graf dan Aplikasinya.pdf?shem=ssusba
  5. A. Maulani and A. K. Lestari, “IMPLEMENTASI PEWARNAAN TITIK PADA PENGELOMPOKKAN PENJUALAN BAHAN GORDEN DI WS INTERIOR,” J. Siger Mat., vol. 4, no. 2, pp. 43–51, 2023.
  6. A. B. Agatha, R. M. Prihandini, and A. P. Kusuma, “Graph Theory: Application of Graphs In Map Coloring,” ResearchGate, 2024.
  7. I. C. Nisa, N. Hinding, and H. Basir, “MODULAR IRREGULAR LABELING ON COMPLETE GRAPHS,” vol. 10 (3), no. Desember, pp. 171–184, 2022, doi: https://doi.org/10.26858/jdm.v10i3.37426.
  8. K. A. Sugeng, Z. Z. Barack, N. Hinding, and R. Simanjuntak, “MODULAR IRREGULAR LABELING ON DOUBLE-STAR AND FRIENDSHIP GRAPHS,” J. Math., vol. 2021, pp. 1–6, 2021, doi: 10.1155/2021/4746609.
  9. G. Chartrand, C. Egan, and P. Zhang, HOW TO LABEL A GRAPH. SPRINGER BRIEFS IN MATHEMATICS, 2019. doi: http://doi.org/10.1007/978-3-030-16863-6.
  10. M. I. Pratama, “NILAI TOTAL KETIDAKTERATURAN SISI DAN TITIK PADA GRAF BERLIAN,” J. Math. Comput. Stat., vol. 4, no. 2, p. 124, 2021, doi: 10.35580/jmathcos.v4i2.34509.
  11. N. R. O. Putri, E. Saputra, and A. A. Lisnasari, “IMPLEMENTATION OF GRAPH COLORING IN UMMUL MUKMININ HIGH SCHOOL STUDENT’S DORMITORY USING WELCH-POWELL ALGORITHM,” BAREKENG J. Math. Its Appl., vol. 17, no. 1, pp. 593–600, 2023.
  12. A. N. Andriani, M. Tonis, and A. Zaky, “OPTIMIZATION OF EMERGENCY INSTALLATION DOCTOR PRACTICE SCHEDULING USING GRAPH COLORING METHOD IN PETALA BUMI HOSPITAL RIAU PROVINCE OPTIMASI PENJADWALAN PRAKTEK DOKTER INSTALASI GAWAT,” vol. 3, no. 2, pp. 1–8, 2022, [Online]. Available: https://journal.univawalbros.ac.id/index.php/jham/article/download/269/142?shem=ssusba
  13. I. Nuroeni, A. I. Kristiana, S. Hussen, S. Setiawani, and R. Adawiyah, “PEWARNAAN TITIK KETAKTERATURAN LOKAL PADA HASIL OPERASI SUBDIVISI GRAF HELM,” J. Difer., vol. 5, no. 2, pp. 117–125, 2023, doi: 10.20473/conmatha.v5i2.47904.
  14. A. I. Kristiana, R. Alfarisi, I. Hesti Agustin, and M. Venkatachalam, “LOCAL IRREGULARITY VERTEX COLORING OF GRAPHS,” Int. J. Civ. Eng. Technol., vol. 10, no. 03, pp. 1606–1616, 2019, [Online]. Available: http://www.iaeme.com/IJCIET/index.asp1606http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=3http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=3
  15. M. Abdy, R. Syam, and T. Tina, “BILANGAN KROMATIK PEWARNAAN TITIK PADA GRAF DUAL DARI GRAF RODA,” J. Math. Comput. Stat., vol. 4, no. 2, p. 95, 2021, doi: 10.35580/jmathcos.v4i2.24443.
  16. R. Adawiyah, M. Aima, and A. I. Kristiana, “ON INCLUSIVE LOCAL IRREGULARITY VERTEX COLORING OF BOOK GRAPH FAMILY,” BAREKENG J. Math. Its Appl., vol. 17, no. 2, pp. 601–608, 2023.
  17. I. L. Mursyidah, Dafik, R. Adawiyah, A. I. Kristiana, and I. H. Agustin, “ON LOCAL IRREGULARITY VERTEX COLORING OF COMB PRODUCT ON STAR GRAPHS,” J. Phys. Conf. Ser., 2021, doi: 10.1088/1742-6596/1836/1/012023.
  18. K. Munawaroh, A. I. Kristiana, E. R. Albirri, Dafik, and R. Adawiyah, “PEWARNAAN TITIK KETAKTERATURAN LOKAL PADA KELUARGA GRAF UNICYCLIC,” CGANT, vol. 2, no. 2, pp. 6–21, 2021, doi: 10.25037/cgantjma.v2i2.59.
  19. M. Hidayat, A. I. Kristiana, R. Adawiyah, Dafik, S. Setiawani, and R. Alfarisi, “ON LOCAL IRREGULARITY OF THE VERTEX COLORING OF THE CORONA PRODUCT OF A TREE GRAPH,” Ural Math. J., vol. 8, no. 2, pp. 94–114, 2022, doi: 10.15826/umj.2022.2.008.
  20. R. F. Sandi, A. I. Kristiana, L. A. Monalisa, Slamin, and R. Adawiyah, “PEWARNAAN TITIK KETAKTERATURAN LOKAL PADA HASIL OPERASI AMALGAMASI TITIK GRAF LINTASAN,” Contemp. Math. Appl., vol. 5, no. 2, pp. 88–101, 2023.
  21. F. Madina and R. Rahadjeng, “PEWARNAAN TITIK KETAKTERATURAN LOKAL PADA BEBERAPA KELAS GRAF,” MATHunesa J. Ilm. Mat., vol. 12, no. 2, pp. 406–417, 2024.
  22. A. Khan, G. Haidar, N. Abbas, M. U. I. Khan, A. U. K. Niazi, and A. U. I. Khan, “METRIC DIMENSIONS OF BICYCLIC GRAPHS,” Mathematics, vol. 11, no. 4, pp. 1–17, 2023, doi: 10.3390/math11040869.
  23. V. Narayanan, “DECOMPOSITION OF BICYCLIC GRAPHS INTO PATHS AND CYCLES,” pp. 1–26, 2022, doi: https://doi.org/10.21203/rs.3.rs-2178974/v1.
  24. A. Ambarwati and V. H. Krisnawati, “CONSTRUCTION OF BICYCLIC GRAPH AND ITS APPLICATION IN TRANS JOGJA ROUTES,” BAREKENG J. Math. Its Appl., vol. 17, no. 4, pp. 2095–2106, 2023.