On topological spaces generated by simple undirected graphs

Hatice Kübra Sarı; Abdullah Kopuzlu; Hatice Kübra Sarı; Abdullah Kopuzlu

doi:10.3934/math.2020355

AIMS Mathematics

2020, Volume 5, Issue 6: 5541-5550. doi: 10.3934/math.2020355

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Research article

On topological spaces generated by simple undirected graphs

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

Received: 22 March 2020 Accepted: 16 June 2020 Published: 29 June 2020
MSC : 54F65, 05C10, 54A05, 97E60

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.
- graph theory,
- topological space,
- homeomorphism,
- equivalence of the graphs
Citation: Hatice Kübra Sarı, Abdullah Kopuzlu. On topological spaces generated by simple undirected graphs[J]. AIMS Mathematics, 2020, 5(6): 5541-5550. doi: 10.3934/math.2020355

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Abstract

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.

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]	H. K. Sarı, A. Kopuzlu, A note on a binary relation corresponding to a bipartite graph, ITM Web Conf., 22 (2018), 01039.

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