On extreme lower approximation neighborhood systems: Application to networks for representing $ X- $ray structures of some chemical compounds

Husniyah Alzubaidi; Husniyah Alzubaidi

doi:10.3934/math.2026431

AIMS Mathematics

2026, Volume 11, Issue 4: 10462-10477. doi: 10.3934/math.2026431

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Research article

On extreme lower approximation neighborhood systems: Application to networks for representing $ X- $ray structures of some chemical compounds

Husniyah Alzubaidi ^,

Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, Saudi Arabia

Received: 21 September 2025 Revised: 19 March 2026 Accepted: 30 March 2026 Published: 16 April 2026
MSC : 05C20, 05C99, 18F60

This paper introduces a new class of topological structures on undirected simple graphs, called extreme graphical topological spaces, using the concepts of extreme systems and lower approximation neighborhood systems. We explore the conditions under which graphs produce either the indiscrete or discrete topology. Several fundamental properties related to both topology and graph theory are examined. Using this framework, along with the concept of extreme outer connectedness in geodesic paths, we define and study new types of connected graphs and discrete spaces, such as extreme maximally connected geodesic graphs and extreme maximally geodesic discrete spaces. Finally, we demonstrate applications of these structures by analyzing the connectedness and discrete characteristics of networks that represent X-ray structures of certain chemical compounds.
- extreme vertices,
- simple graph,
- connectedness,
- topology
Citation: Husniyah Alzubaidi. On extreme lower approximation neighborhood systems: Application to networks for representing $ X- $ray structures of some chemical compounds[J]. AIMS Mathematics, 2026, 11(4): 10462-10477. doi: 10.3934/math.2026431

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Abstract

This paper introduces a new class of topological structures on undirected simple graphs, called extreme graphical topological spaces, using the concepts of extreme systems and lower approximation neighborhood systems. We explore the conditions under which graphs produce either the indiscrete or discrete topology. Several fundamental properties related to both topology and graph theory are examined. Using this framework, along with the concept of extreme outer connectedness in geodesic paths, we define and study new types of connected graphs and discrete spaces, such as extreme maximally connected geodesic graphs and extreme maximally geodesic discrete spaces. Finally, we demonstrate applications of these structures by analyzing the connectedness and discrete characteristics of networks that represent X-ray structures of certain chemical compounds.

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