On b-Coloring of Unicyclic and Bicyclic Graphs

Authors

  • Ridho Alfarisi Department of Mathematics, Universitas Jember, Jl. Kalimantan No. 37, Jember 68121, INDONESIA
  • Sharifah Kartini Said Husain Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MALAYSIA
  • Arika Indah Kristiana Department of Mathematics Education, Universitas Jember, Jl. Kalimantan No. 37, Jember 68121, INDONESIA
  • Witriany Basri Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MALAYSIA

DOI:

https://doi.org/10.17576/jqma.2104.2025.08

Keywords:

b-coloring, b-chromatic number, unicyclic, bicyclic

Abstract

The present work focuses on establishing the b-coloring characteristics of both unicyclic and bicyclic graphs. Recall that a b-coloring of a graph G using k distinct colors is a valid k-coloring where every color partition contains at least one vertex adjacent to vertices of all k − 1 other color classes. The b-chromatic number of G, symbolized as φ(G), represents the highest integer k for which such a b-coloring of G is feasible. In this paper, we determine the b-coloring of unicyclic and bicyclic graphs.

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Published

12-12-2025

How to Cite

Alfarisi, R., Said Husain, S. K., Kristiana, A. I., & Basri, W. (2025). On b-Coloring of Unicyclic and Bicyclic Graphs. Journal of Quality Measurement and Analysis, 21(4), 135–143. https://doi.org/10.17576/jqma.2104.2025.08

Issue

Vol. 21 No. 4 (2025)

Section

Articles

License

This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

This license permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.