A study on graph topology

Document Type : Original paper

Authors

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

2 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 TG. 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.

Keywords

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.
Communications in Combinatorics and Optimization
Volume 8, Issue 2
June 2023
Pages 397-409

Files

Share

How to cite

Statistics