Affiliation:
1. Department of Mathematics, University of Al-Qadisiyah, College of Education, Al Diwaniyah, Iraq
Abstract
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.
Reference13 articles.
1. 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
2. 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
3. T. K. Majumdar, A uniform topological structure on a graph and its properties, Ph.D thesis, India, 1983
4. A. Subramaninan, Studies in graph theory - topological graphs and related topics, Ph.D. thesis, Manonmaniam Sundaranar University, India, 2001
5. S. P. Subbaih, A study of graph theory: topology, steiner domination and semigraph concepts, Ph.D. thesis, Madurai Kamaraj University, India, 2007.