On the <i>r</i>-dynamic coloring of the direct product of a path with either a complete graph or a wheel graph

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

doi:10.3934/math.2021090

AIMS Mathematics

2021, Volume 6, Issue 2: 1470-1496. doi: 10.3934/math.2021090

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On the r-dynamic coloring of the direct product of a path with either a complete graph or a wheel graph

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

Received: 11 September 2020 Accepted: 19 November 2020 Published: 20 November 2020
MSC : 05C15

In this paper, it is explicitly determined the r-dynamic chromatic number of the direct product of any given path with either a complete graph or a wheel graph. Illustrative examples are shown for each one of the cases that are studied throughout the paper.
- r-dynamic coloring,
- direct product,
- path,
- complete graph,
- wheel graph
Citation: T. Deepa, Raúl M. Falcón, M. Venkatachalam. On the r-dynamic coloring of the direct product of a path with either a complete graph or a wheel graph[J]. AIMS Mathematics, 2021, 6(2): 1470-1496. doi: 10.3934/math.2021090

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Abstract

In this paper, it is explicitly determined the r-dynamic chromatic number of the direct product of any given path with either a complete graph or a wheel graph. Illustrative examples are shown for each one of the cases that are studied throughout the paper.

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