A study on graph topology

The concept of topology defined on a set can be extended to the field of graph theory by defining the notion of graph topologies on graphs where we consider a collection of subgraphs of a graph $G$ in such a way that this collection satisfies the three conditions stated similarly to that of the three axioms of point-set topology. This paper discusses an introduction and basic concepts to the graph topology. A subgraph of $G$ is said to be open if it is in the graph topology $mathscr{T}_G$. The paper also introduces the concept of the closed graph and the closure of graph topology in graph topological space using the ideas of decomposition-complement and neighborhood-complement.