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.
This paper presents a method of constructing topologies on the vertex set of a graph G induced by open balls with respect to the graph metric viz. geodesic distance, detour distance, circular distance and circular D-distance on the vertex set of G. Also, this paper explores the topologies induced by eccentric neighbourhoods of vertices of a graph and presents the nature of topologies generated by various graph metrics on the vertex set of some standard graphs.
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