Adjacency and Distance Characteristic Soft Topology on Soft Graphs: Properties and Fundamental Results
DOI:
https://doi.org/10.29304/jqcsm.2026.18.22478Keywords:
Soft graph, Soft topology, Adjacency vertex, Adjacency and Distance Characteristic Soft Topology, Clouser, interiorAbstract
In this paper, we study the Adjacency and Distance Characteristic Soft Topology on soft graphs. This topology is constructed by combining adjacency and distance relations between vertices within the framework of soft sets. We reformulate the notions of closure and interior in a manner consistent with classical topology and investigate their behavior in the soft graph setting. It is shown that both operators are completely determined by adjacency relations. Several fundamental properties are established and supported by illustrative examples. In addition, the connectedness of the proposed topology is examined, highlighting the relationship between graph structure and topological properties.
Downloads
References
D. Molodtsov, “Soft Set Theory First Results,” 1999.
M. Akram and S. Nawaz, “Operations on Soft Graphs,” Fuzzy Information and Engineering, vol. 7, no. 4, pp. 423–449, Dec. 2015, doi: 10.1016/j.fiae.2015.11.003.
K. Palani, T. Jones, and V. Maheswari, “Soft Graphs of Certain Graphs,” in Journal of Physics: Conference Series, IOP Publishing Ltd, Aug. 2021. doi: 10.1088/1742-6596/1947/1/012045.
R. K. Thumbakara, J. Jose, and B. George, “Hamiltonian Soft Graphs.”
J. D. Thenge, B. S. Reddy, and R. S. Jain, “Connected Soft Graph,” New Mathematics and Natural Computation, vol. 16, no. 2, pp. 305–318, Jul. 2020, doi: 10.1142/S1793005720500180.
P. Sharma, N. Bhardwaj, and G. Dhiman, “WITHDRAWN: Alexandroff soft topological spaces,” Mater Today Proc, Feb. 2021, doi: 10.1016/j.matpr.2021.01.351.
S. Hussain and B. Ahmad, “Soft separation axioms in soft topological spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 3, pp. 559–568, 2015, doi: 10.15672/HJMS.2015449426.
Z. I. Mousa, A. F. Hassan, and A. M. Jafar, “II-Bitopology, II-Induced Topology and II-Separation Axioms on Locally Finite Graphs,” Mathematical Modelling of Engineering Problems, vol. 12, no. 3, pp. 1064–1070, 2025, doi: 10.18280/MMEP.120333.
I. Abbas Ali and A. Flieh Hassan, “Adjacency and Distance Characteristic Soft Topology on Soft Graph.” Accepted for publication in International Conference for Physics and Advance Computation Sciences (ICPAS_2025), a journal AIP.
Lenovo, “6. GMN-480[2]-V21N2.” [Online]. Available: http://www.geman.in
M. Shabir and M. Naz, “On soft topological spaces,” Computers and Mathematics with Applications, vol. 61, no. 7, pp. 1786–1799, Apr. 2011, doi: 10.1016/j.camwa.2011.02.006.
K. Ruohonen, “GRAPH THEORY.”
S. Nada, A. E. F. El Atik, and M. Atef, “New types of topological structures via graphs,” in Mathematical Methods in the Applied Sciences, John Wiley and Sons Ltd, Oct. 2018, pp. 5801–5810. doi: 10.1002/mma.4726.
H. L. Yang, X. Liaoy, and S. G. Liz, “On soft continuous mappings and soft connectedness of soft topological spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 2, pp. 385–398, 2015, doi: 10.15672/HJMS.2015459876.
A. Huang and W. Zhu, “Connectedness of graphs and its application to connected matroids through covering-based rough sets,” Dec. 2013, [Online]. Available: http://arxiv.org/abs/1312.4234
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Iman Abbas Ali, Asmhan Flieh Hassan
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
