Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 8 2 2023 06 01 A study on graph topology 397 409 14384 10.22049/cco.2022.27399.1253 EN Achu Aniyan Department of Mathematics, Christ University, Bangalore, India. Sudev Naduvath Christ University, Bangalore, India. Journal Article 2021 09 03 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. https://comb-opt.azaruniv.ac.ir/article_14384_dfabbf33ad159d17be9eeda407eafc66.pdf