초록
In the theory of undirected simple graphs, we introduce the concept of adjacent topological spaces and analyze the minimization of open sets within these spaces. We define the continuity property of mappings between two adjacent topological spaces associated with undirected simple graphs and explore the connections between homeomorphic adjacent topological spaces and isomorphic graphs. Additionally, we investigate the compactness of adjacent topological spaces and examine the relationship between the connectedness of these spaces and the graphs.