Out-graphic topology on directed graphs
Abstract
In this paper, we define a topology TGout, for a digraph G = (V,E) without isolated vertices called out-graphic topology, on the vertices’ set. When the graph is locally finite, T out G will be an Alexandroff topology and we give some characterisations of the minimal basis. Then, we give some open sets and some closed ones. Functions between digraphs are studied and also those between graphic topological spaces and the relations between them. Finally, for a strongly connected digraph, we prove that the topological space (V,TGout) can be disconnected but in other cases can be connected.
Copyright © 2023 Hanan Omer Zomam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
H. O. Zomam, Out-graphic topology on directed graphs, J. Math. Comput. Sci. 13 (2023), 14. https://doi.org/10.28919/jmcs/8189
BibTeX
@article{Zomam2023,
author = {Zomam, Hanan Omer},
title = {Out-graphic topology on directed graphs},
journal = {J. Math. Comput. Sci.},
volume = {13},
year = {2023},
pages = {14},
doi = {10.28919/jmcs/8189}
}