Topological Structures on Vertex Set of Digraphs

Authors

K. Lalithambigai, Department of Mathematics, Sri Kaliswari College (Autonomous-affiliated to Madurai Kamaraj University), Sivakasi, Tamil Nadu, India.Follow
P. Gnanachandra, Centre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College(Autonomous-affiliated to Madurai Kamaraj University), Sivakasi, Tamil Nadu, India.Follow

Abstract

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation on a set can always be represented by a digraph. Topology on a set can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

Keywords

Basis for a topology, Closure, Digraph, Interior, Subbasis for a topology

Article Type

Special Issue Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Lalithambigai, K. and Gnanachandra, P. (2023) "Topological Structures on Vertex Set of Digraphs," Baghdad Science Journal: Vol. 20: Iss. 1, Article 49.
DOI: https://doi.org/10.21123/bsj.2023.8432