Pathless directed topology in connection to the circulation of blood in the heart of human body

AIMS Mathematics

article

Hakeem A. Othman¹  Mohammed M. Al-Shamiri³  Amin Saif⁵  Santanu Acharjee⁶  Tarik Lamoudan³  Rashad Ismail³ 

[1] Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University;Department of Mathematics, Rada'a College of Education and Science, Albaydha University;Department of Mathematics, Faculty of Sciences and Arts, Mahayl Assir, King Khalid University;Department of Mathematics, Faculty of Sciences, Ibb University;Department of Mathematics, Faculty of Applied Sciences, Taiz University;Department of Mathematics, Gauhati University

关键词: pathless directed topology;    directed graphs;    Alexandroff topology;    blood circulation;    heart;   

DOI  :  10.3934/math.2022999

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

We introduce a topology on the set of vertices of a directed graph and we call the topological space as pathless directed topological space. We study relation between the relative topologies and pathless directed topological spaces of E-generated subdirected graphs. Then, we study connectedness, isomorphic and homeomorphic properties in digraphs and pathless directed topological spaces. Moreover, we apply our results to blood circulation process in human heart and disprove Shokry and Aly [M. Shokry and R. E. Aly, Topological properties on graph vs medical application in human heart, Int. J. Appl. Math., 15 (2013), 1103-1109], Nada et al. [S. Nada, A. E. F. El Atik and M. Atef, New types of topological structures via graphs, Math. Method. Appl. Sci., 41 (2018), 5801-5810] and Nawar et al. [A. S. Nawar and A. E. F. A. El-Atik, A model of a human heart via graph nano topological spaces, Int. J. Biomath., 12 (2019), p.1950006]. We show that pathless directed topology is accurately describing the circulation of blood in the heart of human body.

【 授权许可】

CC BY