Characterization of α-open set and α-closure operator via digraph

Abstract In this paper, authors defined a conical open set’s characterization. As a consequence, they introduced the (- space and - space)-open subdigraph in graph theory. Their interrelationships were investigated. As a result, several theorems have been proven. The aim of this paper, is to find graph theory applications due to the difficulty in finding applications in topological spaces, which are pure mathematics branches. We defined a conical open set’s characterization. As a consequence, we introduced the ( space and - space )-open subdigraph in graph theory. Their interrelationships were investigated. As a result, several theorems have been proven.