Spanning graph topology of graphs

The collection of subgraphs of a graph [Formula: see text] containing [Formula: see text] and the null graph [Formula: see text], which is closed under union and intersection, is said to be a graph topology defined on [Formula: see text]. In this paper, we investigate the idea of spanning graph topology of a graph [Formula: see text], where we consider the collection of spanning subgraphs of [Formula: see text] satisfying the axioms analogous to the axioms of graph topology. We begin with the basic concepts of spanning graph topological space and later and introduce two spanning subgraph complements to define closed graphs in spanning graph topological spaces.