On topological structures of the simple undirected graphs

Kopuzlu A.

MATHEMATICAL ANALYSIS, DIFFERENTIAL EQUATION & APPLICATIONS - MADEA 9, Bishkek, Kırgızistan, 21 - 25 Haziran 2021, ss.65

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Bishkek
  • Basıldığı Ülke: Kırgızistan
  • Sayfa Sayıları: ss.65
  • Atatürk Üniversitesi Adresli: Evet

Özet

Graph theory is a branch of mathematics. The theory has also a very important place in our lives, since the graphs are used effectively in many fields. As a result of this, the topological structure of the graphs has been a interesting research subject. Many researchers has studied on this subject. In this paper, we investigate some topological notions such as accumulation point, interior point, relative topology, T0,T1 and Hausdorff space on the topological spaces generated the graphs. Firstly, it is examined that the states of being an accumulation point and an interior point of a point in these spaces. Relative topology on a subgraph of a graph is defined. It is shown that this topology is not equal to the topology generated by this subgraph. Finally, necessary and sufficient conditions for being 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 .