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<p>This paper deals with the <italic>r</italic>-dynamic chromatic problem of the direct product of a path with a fan graph <italic>F</italic><italic><sub>m,n</sub></italic>. The problem is completely solved except for the case <italic>n&lt;r</italic> ∈<italic>{</italic>2<italic>m</italic> +2, 2<italic>m</italic> +3<italic>}</italic>, which is solved under certain assumptions. It enables us to determine in particular the dynamic chromatic number concerning this problem, for all <italic>r ≤</italic> 7, and also, for all <italic>m</italic> ∈<italic>{</italic>1, 2<italic>}</italic>.</p>
</abstract>

This paper deals with the r-dynamic chromatic problem of the direct product of a path with a fan graph Fm,n. The problem is completely solved except for the case n<r ∈{2m +2, 2m +3}, which is solved under certain assumptions. It enables us to determine in particular the dynamic chromatic number concerning this problem, for all r ≤ 7, and also, for all m ∈{1, 2}.

Solving the dynamic coloring problem for direct products of paths with fan graphs

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

This paper deals with the r-dynamic chromatic problem of the direct product of a path with a fan graph Fm,n. The problem is completely solved except for the...

Solving the dynamic coloring problem for direct products of paths with fan graphs

Published Online: Feb 04, 2023

Page range: 115 - 142

Received: Jan 05, 2022

Accepted: Jul 04, 2022

DOI: https://doi.org/10.2478/auom-2023-0006

Keywords
Dynamic coloring problem, direct product, path, fan graph

© 2023 Raúl M. Falcón et al., published by Sciendo

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

Solving the dynamic coloring problem for direct products of paths with fan graphs

Published Online: Feb 04, 2023

Page range: 115 - 142

Received: Jan 05, 2022

Accepted: Jul 04, 2022

DOI: https://doi.org/10.2478/auom-2023-0006

KeywordsDynamic coloring problem, direct product, path, fan graph

© 2023 Raúl M. Falcón et al., published by Sciendo

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

Keywords
Dynamic coloring problem, direct product, path, fan graph