Research article

On topological spaces generated by simple undirected graphs

  • 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.

    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

    Related Papers:

  • 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.


    加载中


    [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.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4022) PDF downloads(573) Cited by(3)

Article outline

Figures and Tables

Figures(4)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog