AIMS Mathematics, 2020, 5(6): 5541-5550. doi: 10.3934/math.2020355.

Researce article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

On topological spaces generated by simple undirected graphs

Department of Mathematics, Faculty of Science, University of Atatürk, Erzurum, 25240, Turkey

In this paper, we study topologies generated by simple undirected graphs without isolated vertices and their properties. We generate firstly a topology using a simple undirected graph without isolated vertices. Moreover, we investigate properties of the topologies generated by certain graphs. Finally,we present continuity and opennes of functions defined from one graph to another via the topologies generated by the graphs. From this point of view, we present necessary and sufficient condition for the topological spaces generated by two different graphs to be homeomorphic.
  Figure/Table
  Supplementary
  Article Metrics

Keywords graph theory; topological space; homeomorphism; equivalence of the graphs

Citation: Hatice Kübra Sarı, Abdullah Kopuzlu. On topological spaces generated by simple undirected graphs. AIMS Mathematics, 2020, 5(6): 5541-5550. doi: 10.3934/math.2020355

References

  • 1. K. A. Abdu, A. Kılıçman, Topologies on the edges set of directed graphs, J. Math. Comput. Sci., 18 (2018), 232-241.    
  • 2. E. A. Abo-Tabl, Rough sets and topological spaces based on similarity, Int. J. Mach. Learn. Cybern., 4 (2013), 451-458.    
  • 3. S. M. Amiri, A. Jafarzadeh, H. Khatibzadeh, An alexandroff topology on graphs, Bull. Iran. Math. Soc., 39 (2013), 647-662.
  • 4. J. A. Bondy, U. S. R. Murty, Graph theory, Graduate Texts in Mathematics, Springer, Berlin, 2008.
  • 5. J. Chen, J. Li, An application of rough sets to graph theory, Inf. Sci., 201 (2012), 114-127.    
  • 6. J. Järvinen, Lattice theory for rough sets, Transactions on Rough Sets VI, LNSC, vol. 4374, Springer-Verlag, Berlin, Heidelberg, 6 (2007), 400-498.
  • 7. S. Lipschutz, Schaum's outline of theory and problems of general topology, Mcgraw-Hill Book Company, New York, St. Louis, San Francisco, Toronto, Sydney, 1965.
  • 8. S. Hatice Kübra, K. Abdullah, A note on a binary relation corresponding to a bipartite graph, ITM Web Conf., 22 (2018), 01039.

 

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved