Embedding Complete Bipartite Graphs into Wheel Related Graphs

A. Berin Greeni; P. Leo Joshwa

doi:10.20965/jaciii.2023.p0645

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JACIII Vol.27 No.4 pp. 645-648

doi: 10.20965/jaciii.2023.p0645

(2023)

Research Paper:

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Embedding Complete Bipartite Graphs into Wheel Related Graphs

A. Berin Greeni and P. Leo Joshwa

School of Advanced Sciences, Vellore Institute of Technology
Vandalur-Kelambakkam Road, Chennai, Tamil Nadu 600127, India

Received:

July 14, 2022

Accepted:

March 28, 2023

Published:

July 20, 2023

Keywords:

embedding, wirelength, complete bipartite graph, wheel graph, gear graph

Abstract

This study considers the exact wirelength of embedding complete bipartite graphs into wheel related graphs such as wheel graphs, gear graphs, and helm graphs.

Cite this article as:

A. Greeni and P. Joshwa, “Embedding Complete Bipartite Graphs into Wheel Related Graphs,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.4, pp. 645-648, 2023.

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References

[1] J. Quadras and S. S. Surya, “Wirelength of circulant networks into wheel related graphs,” Annals of Pure and Applied Mathematics, Vol.14, No.1, pp. 69-75, 2017. https://doi.org/10.22457/apam.v14n1a9
[2] S. L. Bezrukov et al., “Embedding of hypercubes into grids,” L. Brim, J. Gruska, and J. Zlatuška (Eds.), “Mathematical Foundations of Computer Science 1998,” pp. 693-701, Springer, 1998. https://doi.org/10.1007/BFb0055820
[3] A. B. Greeni and I. Rajasingh, “Embedding complete bipartite graph into grid with optimum congestion and wirelength,” Int. J. of Networking and Virtual Organisations, Vol.17, No.1, pp. 64-75, 2017. https://doi.org/10.1504/IJNVO.2017.083544
[4] A. B. Greeni, “Embedding complete bipartite graphs into necklace graphs,” Procedia Computer Science, Vol.172, pp. 199-203, 2020. https://doi.org/10.1016/j.procs.2020.05.031
[5] A. B. Greeni, “Embedding complete bipartite graph into sibling trees with optimum wirelength,” J. of Combinatorial Mathematics and Combinatorial Computing, Vol.112, pp. 115-125, 2020.
[6] M. Miller et al., “Minimum linear arrangement of incomplete hypercubes,” The Computer J., Vol.58, No.2, pp. 331-337, 2015. https://doi.org/10.1093/comjnl/bxu031
[7] P. Manuel et al., “Exact wirelength of hypercubes on a grid,” Discrete Applied Mathematics, Vol.157, No.7, pp. 1486-1495, 2009. https://doi.org/10.1016/j.dam.2008.09.013
[8] M. Arockiaraj et al., “Wirelength of 1-fault Hamiltonian graphs into wheels and fans,” Information Processing Letters, Vol.111, No.18, pp. 921-925, 2011. https://doi.org/10.1016/j.ipl.2011.06.011

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. Quadras and S. S. Surya, “Wirelength of circulant networks into wheel related graphs,” Annals of Pure and Applied Mathematics, Vol.14, No.1, pp. 69-75, 2017. https://doi.org/10.22457/apam.v14n1a9

[2] [2] S. L. Bezrukov et al., “Embedding of hypercubes into grids,” L. Brim, J. Gruska, and J. Zlatuška (Eds.), “Mathematical Foundations of Computer Science 1998,” pp. 693-701, Springer, 1998. https://doi.org/10.1007/BFb0055820

[3] [3] A. B. Greeni and I. Rajasingh, “Embedding complete bipartite graph into grid with optimum congestion and wirelength,” Int. J. of Networking and Virtual Organisations, Vol.17, No.1, pp. 64-75, 2017. https://doi.org/10.1504/IJNVO.2017.083544

[4] [4] A. B. Greeni, “Embedding complete bipartite graphs into necklace graphs,” Procedia Computer Science, Vol.172, pp. 199-203, 2020. https://doi.org/10.1016/j.procs.2020.05.031

[5] [5] A. B. Greeni, “Embedding complete bipartite graph into sibling trees with optimum wirelength,” J. of Combinatorial Mathematics and Combinatorial Computing, Vol.112, pp. 115-125, 2020.

[6] [6] M. Miller et al., “Minimum linear arrangement of incomplete hypercubes,” The Computer J., Vol.58, No.2, pp. 331-337, 2015. https://doi.org/10.1093/comjnl/bxu031

[7] [7] P. Manuel et al., “Exact wirelength of hypercubes on a grid,” Discrete Applied Mathematics, Vol.157, No.7, pp. 1486-1495, 2009. https://doi.org/10.1016/j.dam.2008.09.013

[8] [8] M. Arockiaraj et al., “Wirelength of 1-fault Hamiltonian graphs into wheels and fans,” Information Processing Letters, Vol.111, No.18, pp. 921-925, 2011. https://doi.org/10.1016/j.ipl.2011.06.011