A Review of Discrete Topological Spaces Using Graph Theory
Keywords:
Graph Theory, Topological Space, Discrete Topology, Properties of Graph, 2020 MSC: 05C69
Abstract
This review aims to study the relationship between discrete topological spaces and graph theory, focusing on the mechanism of applying topological concepts within the framework of graph theory. This study also provides a comparative analysis of previous works, highlighting the gaps in the current literature, and exploring the positive aspects. This study aims to give the reader a comprehensive understanding of the literature related to discrete topological spaces and the graph field. This review also emphasizes the possibility of making this literature a starting point for future applications, such as in complex networks and large-scale graphs.
References
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Hamza, Abedal-Hamza Mahdi, and Saba Nazar Faisel Al-khafaji. "Construction a topology on graphs." Journal of Al-Qadisiyah for computer science and mathematics 5.2 (2013): 39-46.
Abdu, Khalid Abdulkalek, and Adem Kilicman. "Topologies on the edges set of directed graphs." International Journal of Mathematical Analysis 12.2 (2018): 71-84.
Neamah, Hussein A., and Khalid Sh Al’Dzhabri. "ODigraphic Topology On Directed Edges." Journal of Al-Qadisiyah for computer science and mathematics 15.1 (2023): Page-74.
Khaleel, Turkan Ahmed, and Ayhan Ahmed Al-Shumam. "A study of graph theory applications in it security." Iraqi Journal of Science (2020): 2705-2714.
Alsinai A, Dhananjayamurthy, Abdlhusein M, Idan M, Cancan M. Topological space generated by edges neighborhoods of discrete topological graphs. European Chemical Bulletin. 2023;12:4270- 4276.
Sarı, Hatice Kübra, and Abdullah Kopuzlu. "On topological spaces generated by simple undirected graphs." Aims Mathematics 5.6 (2020): 5541-5550.
Al’Dzhabri, Khalid Shea Khairallah, and Mohammad Falih Hani Al’murshidy. "On Certain Types of Topological Spaces Associated with Digraphs." Journal of Physics: Conference Series. Vol. 1591. No. 1. IOP Publishing, 2020.
Abdlhusein, Mohammed A., and Manal N. Al-Harere. "Total pitchfork domination and its inverse in graphs." Discrete Mathematics, Algorithms and Applications 13.04 (2021): 2150038.
Abdlhusein, Mohammed A. "Stability of inverse pitchfork domination." International Journal of Nonlinear Analysis and Applications 12.1 (2021): 1009-1016.
Abdulhasan, Zinah H., and Mohammed A. Abdlhusein. "An inverse triple effect domination in graphs." International Journal of Nonlinear Analysis and Applications 12.2 (2021): 913-919.
JWAIR, ZAINAB N., and MOHAMMED A. ABDLHUSEIN. "The neighborhood topology converted from the undirected graphs." Proceedings of IAM 11.2 (2022): 120-128.
Jasim, Taha H., Sami Abdullah Abed, and A. Ghazi. "Concepts of bi-supra topological space via graph theory." Wasit J. Comput. Math. Sci 1.2 (2022).
Abdlhusein, Mohammed A., and Suha J. Radhi. "The arrow edge domination in graphs." International Journal of Nonlinear Analysis and Applications 13.2 (2022): 591-597.
Tariq, AL Sifa Khudir Hamayd-Ridab. "The Graph Of Some Types Of Topological Spaces." Iraqi Journal of Humanitarian, Social and Scientific Research 3.11A (2023).
Neamah, Hussein A., and Khalid Sh Al’Dzhabri. "ODigraphic Topology On Directed Edges." Journal of Al-Qadisiyah for computer science and mathematics 15.1 (2023): Page-74.
Neamah, Hussein A., and Khalid Sh Al’Dzhabri. "Outtopological Digraph Space and Some Related Properties." Earthline Journal of Mathematical Sciences 11.2 (2023): 361-373.
Sarı, Hatice Kübra. "Some properties of the topological spaces generated from the simple undirected graphs." Sigma Journal of Engineering and Natural Sciences 41.2 (2019): 266-270.
Idan, Mays K., and Mohammed A. Abdlhusein. "Some dominating results of the join and corona operations between discrete topological graphs." International Journal of Nonlinear Analysis and Applications 14.5 (2023): 235-242.
Jwair, Zainab Naeem, and Mohammed Abdali Abdlhusein. "Constructing new topological graph with several properties." Iraqi Journal of Science (2023): 2991-2999.
Obayes, K. "K. Construction of Graphs from the Complement of Discrete Topological Space." Central Asian Journal of Mathematical Theory and Computer Sciences 5.3 (2024): 309-319.
Obayes, Karrar Khudhair, Yaqoob A. Farawi, and Ghadeer Khudhair Obayes. "Using Graphs to Depict Relationships among Elements in Various Topological Spaces." Nanotechnology Perceptions (2024): 800-808.
Obayes, Karrar Khudhair. "Text Encryption with Graph Theory Based Key Generation." Journal of Al-Qadisiyah for Computer Science and Mathematics 16.3 (2024): 26-35.
Alaeiyan, Mehdi, Karrar Khudhair Obayes, and Mohammadhadi Alaeiyan. "Prediction nullity of graph using data mining: Prediction nullity of graph using data mining." Results in Nonlinear Analysis 6.2 (2023): 1-8.
Hamza, Abedal-Hamza Mahdi, and Saba Nazar Faisel Al-khafaji. "Construction a topology on graphs." Journal of Al-Qadisiyah for computer science and mathematics 5.2 (2013): 39-46.
Abdu, Khalid Abdulkalek, and Adem Kilicman. "Topologies on the edges set of directed graphs." International Journal of Mathematical Analysis 12.2 (2018): 71-84.
Neamah, Hussein A., and Khalid Sh Al’Dzhabri. "ODigraphic Topology On Directed Edges." Journal of Al-Qadisiyah for computer science and mathematics 15.1 (2023): Page-74.
Khaleel, Turkan Ahmed, and Ayhan Ahmed Al-Shumam. "A study of graph theory applications in it security." Iraqi Journal of Science (2020): 2705-2714.
Alsinai A, Dhananjayamurthy, Abdlhusein M, Idan M, Cancan M. Topological space generated by edges neighborhoods of discrete topological graphs. European Chemical Bulletin. 2023;12:4270- 4276.
Sarı, Hatice Kübra, and Abdullah Kopuzlu. "On topological spaces generated by simple undirected graphs." Aims Mathematics 5.6 (2020): 5541-5550.
Al’Dzhabri, Khalid Shea Khairallah, and Mohammad Falih Hani Al’murshidy. "On Certain Types of Topological Spaces Associated with Digraphs." Journal of Physics: Conference Series. Vol. 1591. No. 1. IOP Publishing, 2020.
Abdlhusein, Mohammed A., and Manal N. Al-Harere. "Total pitchfork domination and its inverse in graphs." Discrete Mathematics, Algorithms and Applications 13.04 (2021): 2150038.
Abdlhusein, Mohammed A. "Stability of inverse pitchfork domination." International Journal of Nonlinear Analysis and Applications 12.1 (2021): 1009-1016.
Abdulhasan, Zinah H., and Mohammed A. Abdlhusein. "An inverse triple effect domination in graphs." International Journal of Nonlinear Analysis and Applications 12.2 (2021): 913-919.
JWAIR, ZAINAB N., and MOHAMMED A. ABDLHUSEIN. "The neighborhood topology converted from the undirected graphs." Proceedings of IAM 11.2 (2022): 120-128.
Jasim, Taha H., Sami Abdullah Abed, and A. Ghazi. "Concepts of bi-supra topological space via graph theory." Wasit J. Comput. Math. Sci 1.2 (2022).
Abdlhusein, Mohammed A., and Suha J. Radhi. "The arrow edge domination in graphs." International Journal of Nonlinear Analysis and Applications 13.2 (2022): 591-597.
Tariq, AL Sifa Khudir Hamayd-Ridab. "The Graph Of Some Types Of Topological Spaces." Iraqi Journal of Humanitarian, Social and Scientific Research 3.11A (2023).
Neamah, Hussein A., and Khalid Sh Al’Dzhabri. "ODigraphic Topology On Directed Edges." Journal of Al-Qadisiyah for computer science and mathematics 15.1 (2023): Page-74.
Neamah, Hussein A., and Khalid Sh Al’Dzhabri. "Outtopological Digraph Space and Some Related Properties." Earthline Journal of Mathematical Sciences 11.2 (2023): 361-373.
Sarı, Hatice Kübra. "Some properties of the topological spaces generated from the simple undirected graphs." Sigma Journal of Engineering and Natural Sciences 41.2 (2019): 266-270.
Idan, Mays K., and Mohammed A. Abdlhusein. "Some dominating results of the join and corona operations between discrete topological graphs." International Journal of Nonlinear Analysis and Applications 14.5 (2023): 235-242.
Jwair, Zainab Naeem, and Mohammed Abdali Abdlhusein. "Constructing new topological graph with several properties." Iraqi Journal of Science (2023): 2991-2999.
Obayes, K. "K. Construction of Graphs from the Complement of Discrete Topological Space." Central Asian Journal of Mathematical Theory and Computer Sciences 5.3 (2024): 309-319.
Obayes, Karrar Khudhair, Yaqoob A. Farawi, and Ghadeer Khudhair Obayes. "Using Graphs to Depict Relationships among Elements in Various Topological Spaces." Nanotechnology Perceptions (2024): 800-808.
Obayes, Karrar Khudhair. "Text Encryption with Graph Theory Based Key Generation." Journal of Al-Qadisiyah for Computer Science and Mathematics 16.3 (2024): 26-35.
Alaeiyan, Mehdi, Karrar Khudhair Obayes, and Mohammadhadi Alaeiyan. "Prediction nullity of graph using data mining: Prediction nullity of graph using data mining." Results in Nonlinear Analysis 6.2 (2023): 1-8.
Published
2024-12-10
How to Cite
Obayes, K., Farawi, Y., & Obayes, G. (2024). A Review of Discrete Topological Spaces Using Graph Theory. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 5(6), 574-583. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/697
Section
Articles
