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In this paper, we determine the <italic>r</italic>-dynamic chromatic number of the fan graph <italic>Fm,n</italic> and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph <italic>M</italic>(<italic>Fm,n</italic>), the total graph <italic>T</italic> (<italic>Fm,n</italic>), the central graph <italic>C</italic>(<italic>Fm,n</italic>) and the line graph <italic>L</italic>(<italic>Fm,n</italic>). In addition, we determine the <italic>r</italic>-dynamic chromatic number of each one of these four families of graphs in case of being <italic>m</italic> = 1.
</abstract>

In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n), the total graph T (Fm,n), the central graph C(Fm,n) and the line graph L(Fm,n). In addition, we determine the r-dynamic chromatic number of each one of these four families of graphs in case of being m = 1.

On the <italic>r</italic>-dynamic coloring of some fan graph families

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

On the -dynamic coloring of some fan graph families

{"article-title":{"italic":"r","content":["On the","-dynamic coloring of some fan graph families"]}}

In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families...

On the r-dynamic coloring of some fan graph families

Published Online: Nov 23, 2021

Page range: 151 - 181

Received: Feb 01, 2021

Accepted: May 15, 2021

DOI: https://doi.org/10.2478/auom-2021-0039

Keywords
-dynamic coloring, fan graph, middle graph, total graph, central graph, line graph

© 2021 Raúl M. Falcón et al., published by Sciendo

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

On the r-dynamic coloring of some fan graph families

Published Online: Nov 23, 2021

Page range: 151 - 181

Received: Feb 01, 2021

Accepted: May 15, 2021

DOI: https://doi.org/10.2478/auom-2021-0039

Keywords-dynamic coloring, fan graph, middle graph, total graph, central graph, line graph

© 2021 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, fan graph, middle graph, total graph, central graph, line graph