New Approach for Closure Spaces on Graphs Based on Relations and Graph Ideals

The main aim of this paper is to combine the connections between graph theory and rough set theory. We created graph ideal ASs by proposing the interior and closure operators, utilizing the concept of graph ideals. With the help of various graphical examples, we applied some topological concepts to the induced graph ideal ASs, including the subspace, continuous functions, lower separation axioms, and connectedness. However, simple directed graphs with or without loops are the ones that are discussed throughout the study. The obtained results are valid for any type of graph: multi-graphs or simple graphs, connected or disconnected graphs, with loops or without loops, and undirected or directed graphs.