Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)

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On b-Coloring of Some Graphs

Authors
A. Z. Magfiroh1, 2, Dafik1, 2, *, A. I. Kristiana1, 2, I. H. Agustin2, 3, I. N. Maylisa2, I. L. Mursyidah2
1Department of Postgraduate Mathematics Education, University of Jember, Jember, Indonesia
2PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
3Department of Mathematics, University of Jember, Jember, Indonesia
*Corresponding author. Email: d.dafik@unej.ac.id
Corresponding Author
Dafik
Available Online 29 June 2024.
DOI
10.2991/978-94-6463-445-7_15How to use a DOI?
Keywords
b-coloring; b-chromatic number; vertex coloring
Abstract

Let G = ( V , E ) be a graph with vertex set V and edge set E. A proper k - v e r t e x coloring of a graph G = ( V , E ) is a partition P = { V 1 , V 2 , . . . V k } of V into independent set. Graph G is b-coloring if there is a vertex in each color class, which is adjacent to at least one vertex in every other color class. The b-chromatic number of graph G, denoted by φ ( G ) , is the largest integer k such that there is a b-coloring with k colors. In this paper, we study b-coloring of king’s tour graph K n , m , tribun graph T n , diamond ladder graph D l n , three cycle ladder graph T C l n , and chain graph K 4 P n .

Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)
Series
Advances in Intelligent Systems Research
Publication Date
29 June 2024
ISBN
10.2991/978-94-6463-445-7_15
ISSN
1951-6851
DOI
10.2991/978-94-6463-445-7_15How to use a DOI?
Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - A. Z. Magfiroh
AU  - Dafik
AU  - A. I. Kristiana
AU  - I. H. Agustin
AU  - I. N. Maylisa
AU  - I. L. Mursyidah
PY  - 2024
DA  - 2024/06/29
TI  - On b-Coloring of Some Graphs
BT  - Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)
PB  - Atlantis Press
SP  - 145
EP  - 154
SN  - 1951-6851
UR  - https://doi.org/10.2991/978-94-6463-445-7_15
DO  - 10.2991/978-94-6463-445-7_15
ID  - Magfiroh2024
ER  -