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

Hatice Kübra Sarı
2022 Sigma Journal of Engineering and Natural Sciences  
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 studied 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
more » ... ferent from the topology generated by this subgraph. Moreover, using the minimal adjacencies of vertices set of a graph, necessary and sufficient conditions for being 𝑇 ! -space, 𝑇 " -space and Hausdorff space of the topological space generated from this graph are presented. This enables to examine whether the topological space is 𝑇 ! , 𝑇 " and Hausdorff without obtaining the topology generated from the graph.
doi:10.14744/sigma.2022.00071 fatcat:h7hx3mncmjbgbk3odhxhjpq72u