Topological approaches of graphs and their applications by neighborhood systems and rough sets

Article type: Research Article

Authors: El Atik, Abd El Fattah A.^{; *} | wahba, Ashgan S.

Affiliations: Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Correspondence: [*] Corresponding author. Abd El Fattah El Atik, Department of mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt. E-mail: aelatik55@yahoo.com.

Abstract: Rough set theory is used in simple directed graphs to study nano topology. Adjacent vertices was used in digraphs only to define their neighborhoods. Four types of neighborhood systems for vertices are introduced in this article which depend on both adjacent vertices and associated edges. Additionally, the generalization of some notions presented by Pawlak and Lellis Thivagar and some of their properties are investigated. Finally, we present a new model of a blood circulation system of the human heart based on blood paths. Also, different kinds of topological separation axioms are presented and studied between vertices and edges of the heart blood circulation model.

Keywords: Graph theory, Rough sets, Nano topology, Human heart, Separation axioms

DOI: 10.3233/JIFS-200126

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 5, pp. 6979-6992, 2020