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Research Article | Open Access

On very strongly perfect Cartesian product graphs

Ganesh Gandal1( ), R Mary Jeya Jothi1, Narayan Phadatare2
Department of Mathematics, Sathyabama Institute of Science and Technology, Chennai-600119, India
Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India
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Abstract

Let G 1 ◻ G 2 be the Cartesian product of simple, connected and finite graphs G 1 and G 2 . We give necessary and sufficient conditions for the Cartesian product of graphs to be very strongly perfect. Further, we introduce and characterize the co-strongly perfect graph. The very strongly perfect graph is implemented in the real-time application of a wireless sensor network to optimize the set of master nodes to communicate and control nodes placed in the field.

Keywords

odd cyclebipartite graphstrong independent setvery strongly perfect graph
CLC number: 05C69, 05C38, 05C40

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2634-2645
DOI: 10.3934/math.2022148

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Cite this article:
Gandal G, Jothi RMJ, Phadatare N. On very strongly perfect Cartesian product graphs. AIMS Mathematics, 2022, 7(2): 2634-2645. https://doi.org/10.3934/math.2022148

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Received: 29 April 2021
Accepted: 05 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)