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The Novel Generally Described Graphs for Cyclic Orthogonal Double Covers of Some Circulants

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Abstract

Circulant graphs nowadays have a vast number of important applications due to the tremendous developments in modern technologies. Interconnection networks are always designed in the form of graphs in which the vertices and edges represent the nodes and links respectively. The circulant graphs that have maximum connectivity edges are called complete graphs. The Cyclic Orthogonal Double Covers (CODC) is a special class of circulant graph decomposition. Many studies proved the existence of CODC by one generating graph. In this paper, the constructing CODCs of complete graphs by copying joint and disjoint unions of new generally described graphs is presented. We consider the use cases of applying the described theory to some problems in various engineering applications. Decomposition of the enormous circulant or complete graphs by copies of disjoint generators enables us to analyze large networks as a set of small networks so that the information is accessed in a fast way.

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ACKNOWLEDGMENTS

The authors acknowledge A.A. Amerikanov for the support provided.

Funding

This research was supported by the Russian Science Foundation (project no. 22-29-00979).

Author information

Authors and Affiliations

  1. Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt

    A. El-Mesady & R. El-Shanawany

  2. Faculty of Systems and Computer Engineering, Al-Azhar University, Cairo, Egypt

    T. Farahat

  3. HSE University, 123458, Moscow, Russia

    A. Y. Romanov

  4. Sevastopol State University, 299053, Sevastopol, Russia

    A. M. Sukhov

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  1. A. El-Mesady
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  2. T. Farahat
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  3. R. El-Shanawany
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  5. A. M. Sukhov
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Corresponding authors

Correspondence to A. El-Mesady, T. Farahat, R. El-Shanawany, A. Y. Romanov or A. M. Sukhov.

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(Submitted by A. M. Elizarov)

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El-Mesady, A., Farahat, T., El-Shanawany, R. et al. The Novel Generally Described Graphs for Cyclic Orthogonal Double Covers of Some Circulants. Lobachevskii J Math 44, 2638–2650 (2023). https://doi.org/10.1134/S1995080223070132

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