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Pure Mathematics for Theoretical Computer Science

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Pure Mathematics for Theoretical Computer Science
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Volume 4Issue 1PP: 08-15 • 2024

Incidence Topological Spaces Generated from The Simple Undirected Graphs

Noor Nouman 1* ,
Faik J. Mayah 2
1Department of Physics, College of Science, Wasit University, Wasit, Iraq
2Department of Mathematics, College of Education for Pure Science, Wasit University, Wasit, Iraq
* Corresponding Author.
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: December 23, 2023 Revised: March 10, 2024 Accepted: May 21, 2024

Abstract

In this paper, we investigate topologies produced by simple connected graphs. In particular, we associate a topology with G, called the incidence topology of G. A sub-base family to generate a incidence topology is implemented on the Vertices V set. Then we analyze some of the properties and discuss the impact topology of a few essential types of graphs. Our motivation in this section is to take a fundamental step towards the investigation of some of the characteristics of simple graphs by their corresponding incidence topology.

Keywords

Finite Topological Spaces Connected Simple Graphs Topologies undirected graphs.

References

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[2]         Shokry, M., & Yousif, Y. Y. (2011). Closure operators on graphs. Journal of Basic and Applied Sciences, Australian, 5(11), 1856-1864.

[3]         Bollobás, B. (2012). Graph theory: an introductory course (Vol. 63). Springer Science & Business Media.

[4]          Wilson, R. J. (1979). Introduction to graph theory. Pearson Education India.

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[6]         Cech, E., Frolik, Z., & Katetov, M. (1966). Topological spaces. Prague: Czechoslovak Academy of Sciences.

[7]         Dikranjan, D., & Tholen, W. (1995). Categorical structure of closure operators, volume 346 of Mathematics and its Applications.

[8]         Birkhoff, G. (1967). Lattice Theory, American Mathematical Colloquium Publications.

[9]         Buszkowski, W. (2004). A Representation Theorem for Co-diagonalizable Algebras. Reports Math. Log., 38, 13-22.

[10]      Vasudev, C. (2006). Graph theory with applications. New Age International.

[11]      J. Dugundji, (1966). Topology, Allyn and Bacon, Inc., Boston.

[12]      Møller, J. M. (2007). General topology. Matematisk Institut, Universitetsparken, 5.

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Nouman, Noor, Mayah, Faik J.. "Incidence Topological Spaces Generated from The Simple Undirected Graphs." Pure Mathematics for Theoretical Computer Science, vol. Volume 4, no. Issue 1, 2024, pp. 08-15. DOI: https://doi.org/10.54216/PMTCS.040101
Nouman, N., Mayah, F. (2024). Incidence Topological Spaces Generated from The Simple Undirected Graphs. Pure Mathematics for Theoretical Computer Science, Volume 4(Issue 1), 08-15. DOI: https://doi.org/10.54216/PMTCS.040101
Nouman, Noor, Mayah, Faik J.. "Incidence Topological Spaces Generated from The Simple Undirected Graphs." Pure Mathematics for Theoretical Computer Science Volume 4, no. Issue 1 (2024): 08-15. DOI: https://doi.org/10.54216/PMTCS.040101
Nouman, N., Mayah, F. (2024) 'Incidence Topological Spaces Generated from The Simple Undirected Graphs', Pure Mathematics for Theoretical Computer Science, Volume 4(Issue 1), pp. 08-15. DOI: https://doi.org/10.54216/PMTCS.040101
Nouman N, Mayah F. Incidence Topological Spaces Generated from The Simple Undirected Graphs. Pure Mathematics for Theoretical Computer Science. 2024;Volume 4(Issue 1):08-15. DOI: https://doi.org/10.54216/PMTCS.040101
N. Nouman, F. Mayah, "Incidence Topological Spaces Generated from The Simple Undirected Graphs," Pure Mathematics for Theoretical Computer Science, vol. Volume 4, no. Issue 1, pp. 08-15, 2024. DOI: https://doi.org/10.54216/PMTCS.040101
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