Construction of Graphs from the Complement of Discrete  Topological Space

Karrar Khudhair Obayes; Yaqoob A. Farawi; Ghadeer Khudhair Obaye

Karrar Khudhair Obayes Department of Computer Information Systems, University of Al-Qadisiyah, Al Diwaniyah, Iraq
Yaqoob A. Farawi Department of Mathematics, University of Thi-Qar, Nasiriyah, Iraq
Ghadeer Khudhair Obaye General Directorate of Education in Al-Qadisiyah, Al Diwaniyah

Keywords: Topological graph, Complement graph, independence number, chromatic number, girth number, clique number, 2020 MSC: 05C69

Abstract

This paper introduces a new idea for constructing graphs from the complement of the discrete topological space, where many of the properties of the aforementioned topological statement were presented, When the number of elements in a non-empty set is two, the corresponding topological expression aligns with that of a null graph. In cases where the set contains three elements the topology statement is compatible with the circuit statement Moreover, we calculated the independent numbers, chromatic number, girth number, and clique number for Complement discrete topological space.

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