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Volume 14
Issue 9
10.3390/axioms14090662
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

On Graph Primal Topological Spaces

by
Dali Shi
1,
Salah E. Abbas
2,*,
Hossam M. Khiamy
2 and
Ismail Ibedou
3,*
1
College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China
2
Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
3
Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
*
Authors to whom correspondence should be addressed.
Axioms 2025, 14(9), 662; https://doi.org/10.3390/axioms14090662
Submission received: 3 June 2025 / Revised: 20 July 2025 / Accepted: 22 August 2025 / Published: 28 August 2025
(This article belongs to the Special Issue Topics in General Topology and Applications)
Versions Notes

Abstract

In this paper, we introduce the concept of the “graph primal,” which serves as the dual structure to the “graph grill”. We present several results associated with graph primal operations. Moreover, we introduce two new graph-local functions on graph adjacency topological spaces (graph ATSs). We then explore the basic properties of the proposed graph-local functions and describe a method for generating two new graph ATSs from existing ones via graph primals. In addition, we examine several fundamental properties and connections of the resulting topologies, supported by some counterexamples. Furthermore, we characterize the nature of the open sets of these new topologies in terms of closure operators. Finally, we assess the compatibility of graph ATSs with the graph primal concept.
Keywords: graph primal; graph local function; graph adjacency topological space graph primal; graph local function; graph adjacency topological space

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MDPI and ACS Style

Shi, D.; Abbas, S.E.; Khiamy, H.M.; Ibedou, I. On Graph Primal Topological Spaces. Axioms 2025, 14, 662. https://doi.org/10.3390/axioms14090662

AMA Style

Shi D, Abbas SE, Khiamy HM, Ibedou I. On Graph Primal Topological Spaces. Axioms. 2025; 14(9):662. https://doi.org/10.3390/axioms14090662

Chicago/Turabian Style

Shi, Dali, Salah E. Abbas, Hossam M. Khiamy, and Ismail Ibedou. 2025. "On Graph Primal Topological Spaces" Axioms 14, no. 9: 662. https://doi.org/10.3390/axioms14090662

APA Style

Shi, D., Abbas, S. E., Khiamy, H. M., & Ibedou, I. (2025). On Graph Primal Topological Spaces. Axioms, 14(9), 662. https://doi.org/10.3390/axioms14090662

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