Graph Ideal Proximity Spaces

Authors

  • D.L. Shi College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China
  • S.E. Abbas Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
  • H.M. Khiamy Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
  • Ismail Ibedou Benha University, Faculty of Science

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i1.7237

Keywords:

graphs, proximity relations, ideals, topology

Abstract

This paper focuses on  extending the concept of "proximity" between sets to graphs. We define graph proximity, graph ideal-proximity spaces. Using the proposed graph ideal proximity spaces, we suggest a new operator over the vertices of a given graph and examine some of their essential aspects. As a result, we obtain  a new topological spaces via this new operator over the vertices of a given  graph.  Comparisons between the obtained topology and  old ones are presented. Further, we not only study some of its properties but also provide some examples. The properties and the implications of related definitions are proposed with examples. Near set theory supplies a major for the classification of members of a set in classes depending on there closeness. We follow the same idea in the graph theory. So, our definitions of graph proximities depend on the nearness of vertices of these graphs. that is we say that to graphs are near if there vertices are near. Based on the idea of nearness between vertices, a real-life application suggested from an information system is provided to demonstrate the significance of this research.

Author Biographies

  • D.L. Shi, College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China

    College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China

  • S.E. Abbas, Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

    Mathematics Department,  Faculty of Science,  Sohag University,  Sohag 82524,  Egypt

  • H.M. Khiamy, Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

    Mathematics Department,  Faculty of Science,  Sohag University,  Sohag 82524,  Egypt

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Published

2026-02-16

Issue

Vol. 19 No. 1: (January 2026)

Section

Topology

License

Copyright (c) 2026 D.L. Shi, S.E. Abbas, H.M. Khiamy, Ismail Ibedou

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How to Cite

Graph Ideal Proximity Spaces. (2026). European Journal of Pure and Applied Mathematics, 19(1), 7237. https://doi.org/10.29020/nybg.ejpam.v19i1.7237