On the <em>r</em>-dynamic coloring of the direct product of a path with either a path or a cycle

T. Deepa; M. Venkatachalam; Raúl M. Falcón; T. Deepa; M. Venkatachalam; Raúl M. Falcón

doi:10.3934/math.2020419

AIMS Mathematics

2020, Volume 5, Issue 6: 6496-6520. doi: 10.3934/math.2020419

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On the r-dynamic coloring of the direct product of a path with either a path or a cycle

1.
Department of Mathematics. Kongunadu Arts and Science College, Tamil Nadu, India
2.
Department of Applied Mathematics I. Universidad de Sevilla, Spain

Received: 16 July 2020 Accepted: 12 August 2020 Published: 20 August 2020
MSC : 05C15

In this paper, we determine explicitly the r-dynamic chromatic number of the direct product of any given path with either a path or a cycle. Illustrative examples are shown for each one of the cases that are studied throughout the paper.
- r-dynamic coloring,
- direct product,
- path,
- cycle
Citation: T. Deepa, M. Venkatachalam, Raúl M. Falcón. On the r-dynamic coloring of the direct product of a path with either a path or a cycle[J]. AIMS Mathematics, 2020, 5(6): 6496-6520. doi: 10.3934/math.2020419

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Abstract

In this paper, we determine explicitly the r-dynamic chromatic number of the direct product of any given path with either a path or a cycle. Illustrative examples are shown for each one of the cases that are studied throughout the paper.

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