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Constructing a Series of Families of Degree Six Circulant Networks

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Abstract

We consider a solution of the problem of constructing a series of families of circulant networks of degree six specified analytically with the help of two parameters one of which is the network diameter. Based on the analysis and generalization of the properties of a new description of an extremal family of circulants, a general series of families of circulant graphs of degree six of arbitrary diameters is constructed that includes extremal circulant graphs of degree six and new infinite families of circulants with an even number of vertices. In the found series of families, descriptions of a series of circulant graphs of any given diameter are analytically determined. Optimality ranges of series graphs are algorithmically identified, where ‘optimal’ is understood as a circulant graph of degree six with the minimum possible diameter for a given number of vertices. The resulting series of families of circulant networks is promising as a scalable topology model for networks on a chip.

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Funding

The study was financially supported by the budget project for the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, project no. 0251–2021–0005.

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  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    E. A. Monakhova & O. G. Monakhov

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  1. E. A. Monakhova
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  2. O. G. Monakhov
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Correspondence to E. A. Monakhova or O. G. Monakhov.

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Translated by V. Potapchouck

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Monakhova, E.A., Monakhov, O.G. Constructing a Series of Families of Degree Six Circulant Networks. J. Appl. Ind. Math. 16, 695–705 (2022). https://doi.org/10.1134/S199047892204010X

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  • DOI: https://doi.org/10.1134/S199047892204010X

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