On Certain Types of Topological Spaces Associated with Digraphs
Khalid Sh. Al’Dzhabri, Mohammad Falih Hani Al’murshidy
Abstract
Abstract In this work, we constructed a new types of topological structures by associated with digraphs called <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">D</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">G</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">σ</mml:mi> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> – topological space and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">D</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">G</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">μ</mml:mi> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> – topological space by induced two alternate definitions DG σ – open set and DG μ – open set respectively. Investigated some properties of the topologies determined by a digraph with respect to each of these alternated definitions.