Distance-based granular computing in networks modeled by intersection graphs

Rehab Alharbi; Hibba Arshad; Imran Javaid; Ali. N. A. Koam; Azeem Haider; Rehab Alharbi; Hibba Arshad; Imran Javaid; Ali. N. A. Koam; Azeem Haider

doi:10.3934/math.2025479

AIMS Mathematics

2025, Volume 10, Issue 5: 10528-10553. doi: 10.3934/math.2025479

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Research article

Distance-based granular computing in networks modeled by intersection graphs

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia
2.
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan

Received: 18 February 2025 Revised: 08 April 2025 Accepted: 18 April 2025 Published: 08 May 2025
MSC : 05A18, 05C12, 05C62

Networks are commonly represented as graphs, where vertices denote entities and edges capture relationships based on shared attributes. Granulation of a network is important for the structural analysis and understanding of its underlying patterns. In this paper, we introduce a distance-based granular computing framework for analyzing networks modeled by intersection graphs. We define these networks as information systems and investigate their granular structures using a distance-based representation. Based on the concepts of indiscernibility between two vertices using the distance from a set, we study indiscernibility partitions on the vertex set. Using the concept of discernibility between vertices, we define the distance-based discernibility matrix and explore its properties. We identify all minimal resolving sets using the discernibility matrix. Furthermore, using the proposed method, we study a transportation network for urban traffic planning.
- granular computing,
- network,
- intersection graphs,
- rough set,
- resolving set,
- reduct,
- discernibility matrix
Citation: Rehab Alharbi, Hibba Arshad, Imran Javaid, Ali. N. A. Koam, Azeem Haider. Distance-based granular computing in networks modeled by intersection graphs[J]. AIMS Mathematics, 2025, 10(5): 10528-10553. doi: 10.3934/math.2025479

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Abstract

Networks are commonly represented as graphs, where vertices denote entities and edges capture relationships based on shared attributes. Granulation of a network is important for the structural analysis and understanding of its underlying patterns. In this paper, we introduce a distance-based granular computing framework for analyzing networks modeled by intersection graphs. We define these networks as information systems and investigate their granular structures using a distance-based representation. Based on the concepts of indiscernibility between two vertices using the distance from a set, we study indiscernibility partitions on the vertex set. Using the concept of discernibility between vertices, we define the distance-based discernibility matrix and explore its properties. We identify all minimal resolving sets using the discernibility matrix. Furthermore, using the proposed method, we study a transportation network for urban traffic planning.

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