Some properties of the topological spaces generated from the simple undirected graphs

Year 2023, Volume: 41 Issue: 2, 266 - 270, 30.04.2023

Hatice Kübra Sarı

Abstract

Graph theory, which is used effectively in many fields from science to liberal arts, has very important place in our lives. As a result of this, the topological structure of the graphs is stud-ied by many researchers. In this paper, we investigate the topological spaces generated by the graphs. The states of being an accumulation point and an interior point of a point in these spaces are examined. It is defined that relative topology on a subgraph of a graph. It is shown that this topology is different from the topology generated by this subgraph. Moreover, using the minimal adjacencies of vertices set of a graph, necessary and sufficient conditions for be-ing 𝑇0 -space, 𝑇1-space and Hausdorff space of the topological space generated from this graph are presented. This enables to examine whether the topological space is 𝑇0, 𝑇1 and Hausdorff without obtaining the topology generated from the graph.

Keywords

Simple Undirected Graphs, Topological Spaces, Graph Theory, Relative Topology

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