b-coloring Analysis on Tree Graph Families
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | b-coloring Analysis on Tree Graph Families |
| 2. | Creator | Author's name, affiliation, country | Rafiantika Megahnia Prihandini; Department of Mathematics Education, Faculty of Teacher Training and Education, Jember University, Jember; Indonesia |
| 2. | Creator | Author's name, affiliation, country | Arika Indah Kristiana; Department of Mathematics Education, Faculty of Teacher Training and Education, Jember University, Jember; Indonesia |
| 2. | Creator | Author's name, affiliation, country | Lusita Risma Dana; Department of Mathematics Education, Faculty of Teacher Training and Education, Jember University, Jember; Indonesia |
| 2. | Creator | Author's name, affiliation, country | Edy Wihardjo; Department of Mathematics Education, Faculty of Teacher Training and Education, Jember University, Jember; Indonesia |
| 2. | Creator | Author's name, affiliation, country | Robiatul Adawiyah; Department of Mathematics Education, Faculty of Teacher Training and Education, Jember University; Indonesia |
| 2. | Creator | Author's name, affiliation, country | Hutkemri Zulnaidi; Department of Mathematics and Sciences Education, Faculty of Education, Universiti Malaya, Kuala Lumpur; Malaysia |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | b-Coloring; b-Chromatic Number; Broom Graph; Banana Tree Graph; Centipede Graph; Tree Graph. |
| 4. | Description | Abstract | A tree graph is a connected graph and has no circuits. Tree graphs used in this study include: broom graph, centipede graph, and Banana Tree graph. Graph coloring is the process of giving color to graph elements with the rule that neighboring elements must not have the same color, and the number of colors used must be as minimal as possible. b-coloring of a graph G is a coloring of the vertices of G such that each color class has at least one vertex adjacent to all other color classes. The b-chromatic number of a graph G is denoted by φ(G), is the largest integer k such that G has a b-coloring with k colors. The limit of b-coloring of graph G with maximum degree ∆(G) is as follows, χ(G) ≤ φ(G) ≤ ∆(G) + 1.χ(G) is the chromatic number of a graph G where χ(G) is the minimum value of the color required for proper coloring of graph G. While ∆(G) is the maximum degree of the vertices in graph G. This study uses an exploratory research type with an axiomatic deductive method and a pattern detection method. Based on this study, the results of the b-coloring analysis on the tree graph family are known. The results of this study are expected to be used as study material and the development of scientific knowledge related to b-coloring analysis on other graphs. |
| 5. | Publisher | Organizing agency, location | Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang |
| 6. | Contributor | Sponsor(s) | |
| 7. | Date | (YYYY-MM-DD) | 2026-05-30 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/32328 |
| 10. | Identifier | Digital Object Identifier (DOI) | https://doi.org/10.18860/cauchy.v11i1.32328 |
| 11. | Source | Title; vol., no. (year) | CAUCHY: Jurnal Matematika Murni dan Aplikasi; Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI |
| 12. | Language | English=en | en |
| 13. | Relation | Supp. Files | |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
| 15. | Rights | Copyright and permissions |
Copyright (c) 2026 Arika Indah Kristiana, Rafiantika Megahnia Prihandini, Lusita Risma Dana, Edy Wihardjo, Robiatul Adawiyah This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. |