On some operations on grey graphs with application

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.