Abstract: Previously, some structures of topologies on graphs were presented on a set of nodes or edges (arcs) only. In this paper, we define a topology on a set of nodes and edges of an undirected graph, and two topologies on a set of nodes and arcs of a directed graph. Moreover, we present some topological properties of these spaces and discuss some relationship between them and the graphs. Also, we show that these topologies satisfy the property of being Alexandroff.
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Keywords and phrases: isomorphic graphs, Alexandroff topology, topological properties.
Received: November 18, 2022; Revised: January 17, 2023; Accepted: January 27, 2023; Published: June 12, 2023
How to cite this article: Mesfer H. Alqahtani, New topologies on a graph, Advances and Applications in Discrete Mathematics 37 (2023), 77-93. http://dx.doi.org/10.17654/0974165823013
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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