Fuzzy strong vertex connectivity and fuzzy strong edge connectivity with their applications

Junye Ma; Xiaoke Han; Tong Ning; Suping Wang; Junye Ma; Xiaoke Han; Tong Ning; Suping Wang

doi:10.3934/math.20261094

AIMS Mathematics

2026, Volume 11, Issue 8: 27351-27369. doi: 10.3934/math.20261094

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Research article

Fuzzy strong vertex connectivity and fuzzy strong edge connectivity with their applications

School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China

Received: 10 June 2026 Revised: 14 August 2026 Accepted: 18 August 2026 Published: 31 August 2026
MSC : 05C72, 05C40, 05C90, 92D40

Conventional connectivity analysis of fuzzy graphs provides a crucial basis for evaluating the transmission reliability of networks. However, the separate consideration of strong paths and strongest paths has become the primary bottleneck in accurately measuring the overall network connectivity performance. This paper takes the strongest strong path as a core starting point. It breaks through the one-dimensional limitations of conventional connectivity evaluation in fuzzy graphs. Accordingly, the concepts of fuzzy strong vertex connectivity and fuzzy strong edge connectivity are defined. On this basis, this paper investigates the quantitative laws of these two types of connectivity in typical fuzzy graphs, constructs standardized calculation algorithms, and clarifies practical application pathways. The research provides solid scientific support for the health evaluation of regional ecosystems and further extends the application foundation of fuzzy graph network simulation methods.
- fuzzy graph,
- strongest strong path,
- strong vertex connectivity,
- strong edge connectivity
Citation: Junye Ma, Xiaoke Han, Tong Ning, Suping Wang. Fuzzy strong vertex connectivity and fuzzy strong edge connectivity with their applications[J]. AIMS Mathematics, 2026, 11(8): 27351-27369. doi: 10.3934/math.20261094

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Abstract

Conventional connectivity analysis of fuzzy graphs provides a crucial basis for evaluating the transmission reliability of networks. However, the separate consideration of strong paths and strongest paths has become the primary bottleneck in accurately measuring the overall network connectivity performance. This paper takes the strongest strong path as a core starting point. It breaks through the one-dimensional limitations of conventional connectivity evaluation in fuzzy graphs. Accordingly, the concepts of fuzzy strong vertex connectivity and fuzzy strong edge connectivity are defined. On this basis, this paper investigates the quantitative laws of these two types of connectivity in typical fuzzy graphs, constructs standardized calculation algorithms, and clarifies practical application pathways. The research provides solid scientific support for the health evaluation of regional ecosystems and further extends the application foundation of fuzzy graph network simulation methods.

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