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

Hakeem A. Othman; Mohammed M. Al-Shamiri; Amin Saif; Santanu Acharjee; Tarik Lamoudan; Rashad Ismail; Hakeem A. Othman; Mohammed M. Al-Shamiri; Amin Saif; Santanu Acharjee; Tarik Lamoudan; Rashad Ismail

doi:10.3934/math.2022999

AIMS Mathematics

2022, Volume 7, Issue 10: 18158-18172. doi: 10.3934/math.2022999

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Research article

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

1.
Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, KSA
2.
Department of Mathematics, Rada'a College of Education and Science, Albaydha University, Yemen
3.
Department of Mathematics, Faculty of Sciences and Arts, Mahayl Assir, King Khalid University, KSA
4.
Department of Mathematics, Faculty of Sciences, Ibb University, Ibb, Yemen
5.
Department of Mathematics, Faculty of Applied Sciences, Taiz University, Taiz, Yemen
6.
Department of Mathematics, Gauhati University, Guwahati-781014, Assam, India

Received: 19 April 2022 Revised: 02 August 2022 Accepted: 03 August 2022 Published: 10 August 2022
MSC : 05C20, 05C99, 54A05, 92B05, 92C42

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.
- pathless directed topology,
- directed graphs,
- Alexandroff topology,
- blood circulation,
- heart
Citation: Hakeem A. Othman, Mohammed M. Al-Shamiri, Amin Saif, Santanu Acharjee, Tarik Lamoudan, Rashad Ismail. Pathless directed topology in connection to the circulation of blood in the heart of human body[J]. AIMS Mathematics, 2022, 7(10): 18158-18172. doi: 10.3934/math.2022999

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Abstract

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.

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