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Let <italic>G</italic> and <italic>H</italic> be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the <italic>b</italic>-chromatic number of every subdivision-vertex neighbourhood corona <italic>G</italic> ⊡ <italic>H</italic> or <italic>G</italic> ⊡ <italic>K</italic>n, where <italic>K</italic>n is the complete graph of order <italic>n</italic>. It is also established for those graphs <italic>K</italic>n ⊡ <italic>G</italic> having <italic>m</italic>-degree not greater than <italic>n</italic> + 2. All the proofs are accompanied by illustrative examples.
</abstract>

Let G and H be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the b-chromatic number of every subdivision-vertex neighbourhood corona G ⊡ H or G ⊡ Kn, where Kn is the complete graph of order n. It is also established for those graphs Kn ⊡ G having m-degree not greater than n + 2. All the proofs are accompanied by illustrative examples.

Determining the <italic>b</italic>-chromatic number of subdivision-vertex neighbourhood coronas

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Determining the -chromatic number of subdivision-vertex neighbourhood coronas

Let G and H be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the b-chromatic number of every subdivision-vertex...

Determining the b-chromatic number of subdivision-vertex neighbourhood coronas

Published Online: Jul 10, 2024

Page range: 53 - 84

Received: Feb 27, 2023

Accepted: Jul 11, 2023

DOI: https://doi.org/10.2478/auom-2024-0019

Keywords
b-chromatic number, subdivision-vertex neighbourhood corona, path, cycle, star, complete graph

© 2024 Raúl M. Falcón et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Determining the b-chromatic number of subdivision-vertex neighbourhood coronas

Published Online: Jul 10, 2024

Page range: 53 - 84

Received: Feb 27, 2023

Accepted: Jul 11, 2023

DOI: https://doi.org/10.2478/auom-2024-0019

Keywordsb-chromatic number, subdivision-vertex neighbourhood corona, path, cycle, star, complete graph

© 2024 Raúl M. Falcón et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
b-chromatic number, subdivision-vertex neighbourhood corona, path, cycle, star, complete graph