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

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 h...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-07, Vol.44 (7), p.2638-2650
Main Authors: El-Mesady, A., Farahat, T., El-Shanawany, R., Romanov, A. Y., Sukhov, A. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Apexes
Copying
Decomposition
Geometry
Graph theory
Graphs
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Networks
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223070132