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MinLA of \((K_9-C_9)^n\) and its optimal layout into certain trees

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Abstract

Embedding deals with simulating one architecture called guest into another called host, as it helps in modifying algorithms designed for the guest graph to be implemented in the host graph. In this paper, we have obtained the optimal wirelength of embedding \((K_9-C_9)^n\) into \(P_{9^n}\) and certain trees, where \((K_9-C_9)^n\) is the Cartesian product of complete graph on 9 vertices with a deletion of a cycle on 9 vertices and \(P_{9^n}\) is a path on \(9^n\) vertices. Furthermore, we have also obtained the wirelength of embedding the Cartesian product graph \((K_9-C_9)^n\) into Banana trees and Firecracker trees.

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Acknowledgements

We would like to thank Dr. Indra Rajasingh, Adjunct Professor, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, for her valuable suggestions. We would like to thank the reviewers for their thoughtful comments and efforts towards improving our manuscript.

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Authors and Affiliations

  1. School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, 600127, India

    Syeda Afiya

  2. School of Computer Science and Engineering, Vellore Institute of Technology, Chennai, Tamil Nadu, 600127, India

    M Rajesh

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  1. Syeda Afiya
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  2. M Rajesh
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The authors confirm their contribution to the paper as follows: study conception and design: MR and SA; theorem analysis and interpretation of results: MR and SA; draft manuscript preparation: MR and SA; all authors reviewed the results and approved the final version of the manuscript.

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Correspondence to M Rajesh.

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Afiya, S., Rajesh, M. MinLA of \((K_9-C_9)^n\) and its optimal layout into certain trees. J Supercomput 79, 12000–12012 (2023). https://doi.org/10.1007/s11227-023-05140-3

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