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On some operations on grey graphs with application

Mohammed Atef (Grey System Research Institute, Nanjing University of Aeronautics and Astronautics, Nanjing, China) (Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt)
Sifeng Liu (Grey System Research Institute, Nanjing University of Aeronautics and Astronautics, Nanjing, China) (School of Management, Northwestern Polytechnical University, Xi’an, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 27 June 2024

Issue publication date: 24 September 2024

51

Abstract

Purpose

The objective of this paper is to formulate the precise meanings of grey graphs and examine some of their properties.

Design/methodology/approach

This article introduces innovative concepts of grey sets based on the grey number. We establish the grey graphs and examine their essential properties as isomorphisms of these graphs. Additionally, we explore the notion of a grey-complete graph and demonstrate certain properties of self-complementary grey-complete graphs.

Findings

We showcase novel facets of grey system theory through the establishment of the structures of grey graphs, and the subsequent analysis of their distinctive traits.

Practical implications

This article provides us with a new theoretical direction for grey system theory according to grey numbers. Thus, we present test examples that explain the routes between cities and the electrical wires between homes. Furthermore, the concept of grey graphs can be applied in several areas of engineering, computer science, neural networks, artificial intelligence, and medical diagnosis.

Originality/value

The proposed concepts are considered novel mathematical directions in grey system theory for the first time. Some operations of grey graphs are also explored.

Keywords

Acknowledgements

This work was supported by a long term project of national major talent plan of China (Grant No. YQR20024), a projects of the National Natural Science Foundation of China (Grant No. 72071111), a project of Intelligence Introduction base of the Ministry of Science and Technology (Grant No. G2021181014L), an original Exploration Project of the Central University Research and Innovation Fund (Grant No. ILA220721A23). At the same time, the authors would like to acknowledge the partial support of the Fundamental Research Funds for the Excellent Innovation Team of Nanjing University of Aeronautics and Astronautics (Grant No. [2022]2-22).

Citation

Atef, M. and Liu, S. (2024), "On some operations on grey graphs with application", Grey Systems: Theory and Application, Vol. 14 No. 4, pp. 789-811. https://doi.org/10.1108/GS-12-2023-0125

Publisher

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Emerald Publishing Limited

Copyright © 2024, Emerald Publishing Limited

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