Outtopological Digraph Space and Some Related Properties

  • Hussein A. Neamah Department of Mathematics, University of Al-Qadisiyah, College of Education, Al Diwaniyah, Iraq
  • Khalid Sh. Al’Dzhabri Department of Mathematics, University of Al-Qadisiyah, College of Education, Al Diwaniyah, Iraq
Keywords: digraph, topology, Alexandroff topology, incident edges system


The outtopological digraph space, a novel topological constraint imposed by a subbasis, is introduced in this work. A subbasis $\overleftarrow{\textrm{I}}^{\alpha}_{\underset{\cdot}{e}}$ is a set contains one vertex such that the edge ẹ is outdegree of it. As a result, various theorems have been established. A characterization and some examples are provided to describe this new structure.


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 spacesassociated 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.

How to Cite
Neamah, H. A., & Al’Dzhabri, K. S. (2023). Outtopological Digraph Space and Some Related Properties. Earthline Journal of Mathematical Sciences, 11(2), 361-373. https://doi.org/10.34198/ejms.11223.361373