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September 17, 2025SymmetryOpen Access

Exploring Symmetry Structures in Integrity-Based Vulnerability Analysis Using Bipolar Fuzzy Graph Theory

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New integrity parameters were defined for bipolar fuzzy graphs, enhancing vulnerability analysis.
The study introduces the node strength sequence, pivotal for understanding graph integrity.
BIPOLAR fuzzy graphs were applied to road networks, highlighting both positive and negative attributes.
Analysis of different graph unions and products illustrated varying integrity results, supporting network resilience.

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This analysis defines integrity using bipolar fuzzy graph theory, revealing its impact on connectivity in networks.

Alhazmi et al. (2025) studied this question.

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