# A study on graph topology

Document Type : Original paper

Authors

1 Christ University, Bangalore, India.

2 Department of Mathematics, Christ University, Bangalore, India.

Abstract

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.

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Main Subjects

#### References

[1] T.J. Ahlborn, On directed graphs and related topological spaces, Ph.D. thesis, Kent State University, USA., 1964.
[2] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, New York, 2008.
[3] R. Diestel, Graph Theory, Springer, New York, 2018.
[4] Chris Godsil and Gordon F Royle, Algebraic Graph Theory, vol. 207, Springer Science & Business Media, 2001.
[5] F. Harary, Graph Theory, Narosa Publ., New Delhi, 1969.
[6] K.D. Joshi, Introduction to General Topology, New Age International, 1983.
[7] W.B.V. Kandasamy and F. Smarandache, Strong Neutrosophic Graphs and Subgraph Topological Subspaces, EuropaNova, 2016.
[8] K. Karunakaran, Topics in graph theory topological approach, Ph.D. thesis, University of Kerala, 2007.
[9] J.L. Kelley, General Topology, Courier Dover Publications, 2017.
[10] J. Munkres, Topology, Pearson Education, 2014.
[11] A.E. Wegner, Subgraph covers: an information-theoretic approach to motif analysis in networks, Physical Review X 4 (2014), no. 4, 041026.
[12] D.B. West, Introduction to Graph Theory, vol. 2, Prentice-Hall of India, New Delhi, 2001.