On topological spaces generated by graphs and vice versa
DOI:
https://doi.org/10.29304/jqcm.2021.13.3.827Keywords:
graph theory, topological spaceAbstract
The relationship between Graph Theory and Topological Space has recently developed greatly , as researchers have been able to find
solutions to some problems in daily life by transforming the problem
into a graph and then generating a topological space and thus facilita-
ting reading the problem and solving it. The researchers also studied
the generation of graph from topological spaces.In this article we will present two types of relations on the edges set that generate topolog-
ical spaces, and we will discuss some properties of this topology, and
we will study discuss the method of returning from the topological
space to the graphs through using previous relationships.
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References
[1] K. A. Abdu, and A. Kılıçman. "Topologies on the edges set of directed graphs." International Journal of Mathematical Analysis 12, no. 2. 2018: 71-84.
[2] J. M. Aldous, and R. J. Wilson. Graphs and applications: an introductory approach. Springer Science & Business Media, 2004.
[3] J. A. Bondy, and Uppaluri Siva Ramachandra Murty. Graph theory with applications. Vol. 290. London: Macmillan, 1976.
[4] Xu, Junming. Theory and application of graphs. Vol. 10. Springer Science & Business Media, 2003.
[5] Xu, Junming. Topological structure and analysis of interconnection networks. Vol. 7. Springer Science & Business Media, 2013.
[6] A.D.E.M., Kilicman, and K H.A.L.I.D. Abdulkalek. "Topological spaces associated with simple graphs." Journal of Mathematical Analysis 9, no. 4. 2018: 44-52.
[7] H.A-H.Mahdi, and S.N.F. Al-khafaji. "Construction A Topology On Graphs." Journal of Al-Qadisiyah for computer science and mathematics 5, no. 2. 2013: 39-46.
[8] A. S., Nawar, and Abd El Fattah A. El Atik. "A model of a human heart via graph nano topological spaces." International Journal of Biomathematics 12, no. 01. 2019: 1950006.
[9] V. N. Ryzhov. "Review of a book on the anniversary of the theory of the Berezinskii–Kosterlitz–Thouless transition—a book which proved to be a precursor of the 2016 Nobel Prize in physics." Physics-Uspekhi 60, no. 1. 2017: 114.
[10] H. K. Sarı, and Abdullah Kopuzlu. "On topological spaces generated by simple undirected graphs [J]." AIMS Mathematics 5, no. 6. 2020: 5541-5550.
[11] M. A. F. Soliman. " Some Topological Applications on Graph Theory and Information Systems." PhD diss.,
Menoufia University, Ja. 25. 2019.
[12] S. A. M. Topology without tears. University of New England, 1989.
[2] J. M. Aldous, and R. J. Wilson. Graphs and applications: an introductory approach. Springer Science & Business Media, 2004.
[3] J. A. Bondy, and Uppaluri Siva Ramachandra Murty. Graph theory with applications. Vol. 290. London: Macmillan, 1976.
[4] Xu, Junming. Theory and application of graphs. Vol. 10. Springer Science & Business Media, 2003.
[5] Xu, Junming. Topological structure and analysis of interconnection networks. Vol. 7. Springer Science & Business Media, 2013.
[6] A.D.E.M., Kilicman, and K H.A.L.I.D. Abdulkalek. "Topological spaces associated with simple graphs." Journal of Mathematical Analysis 9, no. 4. 2018: 44-52.
[7] H.A-H.Mahdi, and S.N.F. Al-khafaji. "Construction A Topology On Graphs." Journal of Al-Qadisiyah for computer science and mathematics 5, no. 2. 2013: 39-46.
[8] A. S., Nawar, and Abd El Fattah A. El Atik. "A model of a human heart via graph nano topological spaces." International Journal of Biomathematics 12, no. 01. 2019: 1950006.
[9] V. N. Ryzhov. "Review of a book on the anniversary of the theory of the Berezinskii–Kosterlitz–Thouless transition—a book which proved to be a precursor of the 2016 Nobel Prize in physics." Physics-Uspekhi 60, no. 1. 2017: 114.
[10] H. K. Sarı, and Abdullah Kopuzlu. "On topological spaces generated by simple undirected graphs [J]." AIMS Mathematics 5, no. 6. 2020: 5541-5550.
[11] M. A. F. Soliman. " Some Topological Applications on Graph Theory and Information Systems." PhD diss.,
Menoufia University, Ja. 25. 2019.
[12] S. A. M. Topology without tears. University of New England, 1989.
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Published
2021-08-08
How to Cite
Ibraheem, T. Q., & Nagim, A. A. (2021). On topological spaces generated by graphs and vice versa. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(3), Math Page 13– 24. https://doi.org/10.29304/jqcm.2021.13.3.827
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Math Articles
