Subspace graph topological space of graphs




graph topology, subspace graph topology, d-closure, nbd-closure


A graph topology defined on a graph G is a collection 𝒯 of subgraphs of G which satisfies the properties such as K0, G ∈ 𝒯 and 𝒯 is closed under arbitrary union and finite intersection. Let (X, T) be a topological space and Y ⊆ X then, TY = {U ∩ Y : U ∈ T} is a topological space called a subspace topology or relative topology defined by T on Y. In this P1 we discusses the subspace or the relative graph topology defined by the graph topology 𝒯 on a subgraph H of G. We also study the properties of subspace graph topologies, open graphs, d-closed graphs and nbd-closed graphs of subspace graph topologies.

Author Biographies

Achu Aniyan, Christ University,

Department of Mathematics.

Sudev Naduvath, Christ University,

Department of Mathematics.


T. Ahlborn, On directed graphs and related topological spaces. PhD thesis, Kent State University, USA., 1964.

W. V. Kandasamy, F. Smarandache, et al., “Strong neutrosophic graphs and subgraph topological subspaces,” arXiv preprint arXiv:1611.00576, 2016.

J. Munkres, Topology. Pearson Education, 2014.

K. D. Joshi, Introduction to general topology. New Age International, 1983.

F. Harary, Graph theory. Narosa Publications, New Delhi, 1969.

D. B. West, Introduction to graph theory, vol. 2. Prentice hall Upper Saddle River, NJ, 1996.

A. Aniyan and S. Naduvath, “A study on graph topology,” communicated, 2020.



How to Cite

A. . Aniyan and S. Naduvath, “Subspace graph topological space of graphs”, Proyecciones (Antofagasta, On line), vol. 42, no. 2, pp. 521-532, Mar. 2023.