New Topological Structure related from Digraph
Abstract
This work introduces a novel topological constraint called the intopological digraph space imposed by a subbasis 
contains one vertice such that the edge ẹ is indegree of it and investigates some properties of this structure. Our objective is to provide a crucial first step in the study of some of the characteristics of digraphs by utilizing the appropriate topology.
References
J.W. Evans, F. Harary and M.S. Lynn, On the computer enumeration of finite topologies, Communications of the ACM 10(5) (1967), 295-297. https://doi.org/10.1145/363282.363311
T.N. Bhargava and T.J. Ahlborn, On topological spaces associated with digraphs, Acta Mathematica Academiae Scientiarum Hungaricae 19 (1968), 47-52. https://doi.org/10.1007/BF01894678
T. K. Majumdar, A uniform topological structure on a graph and its properties, Ph.D thesis, India, 1983
A Subramaninan, Studies in graph theory - topological graphs and related topics, Ph.D. thesis, Manonmaniam Sundaranar University, India, 2001
S. P. Subbaih, A study of graph theory: topology, steiner domination and semigraph concepts, Ph.D. thesis, Madurai Kamaraj University, India, 2007.
K. Karunakaran, Topics in graph theory-topological approach, Ph.D. thesis, University of Kerala, India, 2007.
U. Thomas, A study on topological set-indexers of graphs, Ph.D. thesis, Mahatma Gandhi University, India, 2013.
M. Shokry, Generating topology on graphs operations on graphs, Applied Mathematical Science 9(54) (2015), 2843-2857. https://doi.org/10.12988/ams.2015.5154.
K.A. Abdu and A. Kilicman, Topologies on the edges sets of directed graphs, International Journal of Mathematical Analysis 12(2) (2018), 71-84. https://doi.org/10.12988/ijma.2018.814
Kh. Sh. Al’Dzhabri, A. M. Hamza and Y. S. Eissa, On DG-topological spaces associated with directed graphs, Journal of Discrete Mathematical Sciences & Cryptography 23(5) (2020), 1039-1046. https://doi.org/10.1080/09720529.2020.1714886
Kh. Sh. Al’Dzhabri and M. F. H. Al’murshidy, On certain types of topological spaces associated with digraphs, Journal of Physics: Conference Series 1591 (2020), 012055. https://doi.org/10.1088/1742-6596/1591/1/012055
S.S. Ray, Graph Theory with Algorithms and its Applications: In Applied Sciences and Technology, Springer, New Delhi, 2013.
J.M. Møller, General Topology, Authors’ Notes, 2007.
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
