Fuzzy topological invariants in uniform fuzzy graphs

Article type: Research Article

Authors: Guan, Hao^a | Ejaz, Farukh^b | ur Rehman, Atiq^{b; *} | Hussain, Muhammad^b | Kosari, Saeed^a

Affiliations: [a] Institute of Computing Science and Technology, Guangzhou university, Guangzhou, China | [b] Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan

Correspondence: [*] Corresponding author. Atiq ur Rehman. E-mail: [email protected].

Abstract:  In this paper, we have defined some fuzzy topological invariants for particular types of uniform fuzzy graph. Some particular useful types of uniform fuzzy graphs are Uniform Edge Fuzzy Graph, Uniform Vertex Fuzzy Graph, Uniform Vertex-Edge Fuzzy Graph and Totally Uniform Fuzzy Graph. For each particular type we have defined different kinds of degrees in a graph in accordance with the unique nature of it. In the end, we have applied all our output results to a cellular neural fuzzy graph as an example, to verify the predicting ability of topological invariants. The aim of this paper is to define more significant fuzzy topological invariants in fuzzy graphs. Our ideas will help to create a link between fuzzy graph theory and simple (crisp) graph theory.

Keywords: Uniform Edge Fuzzy Graphs, Fuzzy Topological Invariants, Fuzzy degrees

DOI: 10.3233/JIFS-223402

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 1, pp. 1653-1662, 2023