Cubic fuzzy graphs : New topological indices and applications in network vulnerability
Rashmi Singhrsingh7@amity.eduDepartment of MathematicsAmity Institute of Applied SciencesAmity UniversityNoida, Uttar Pradesh, 201303, IndiaView full profile → , Khursheed AlamDepartment of Mathematics & Data ScienceThe A. H. Siddiqi Centre for Advanced Research in Applied Mathematics & Physics (CARAMP)Sharda UniversityGreater Noida, Uttar Pradesh, 201303, IndiaView full profile → , Masood Alammalam@squ.edu.omDepartment of Mathematics & Information TechnologyCenter for Preparatory StudiesSultan Qaboos UniversityMuscat, 123, Sultanate of OmanView full profile → , *Neha BhardwajCorresponding authornehabhr1807@gmail.comDepartment of MathematicsAmity Institute of Applied SciencesAmity UniversityNoida, Uttar Pradesh, 201303, IndiaView full profile →
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- Received:
- 01 Jan 2026
- Published Online:
- 30 Sep 2026
- Language:
- EN
- Article no.:
- JDMSC-2862
- Pages:
- 3463–3474
Abstract
The analysis of complex networks under uncertainty represents a fundamental challenge in modern graph theory and network science. This paper introduces a comprehensive framework for computing topological indices on cubic fuzzy graphs (CFGs), which simultaneously incorporate interval-valued and point-valued fuzzy memberships, providing a richer mathematical structure for modeling uncertainty in network systems. We define five novel topological indices for CFGs: the Cubic Fuzzy Wiener Index (CFWI), Cubic Fuzzy First Zagreb Index (CFM1), Cubic Fuzzy Second Zagreb Index (CFM2), Cubic Fuzzy Randić Index (CFR), and Cubic Fuzzy Sombor Index (CFSO). For each index, we provide formal definitions, derive computational formulas, and establish theoretical properties through rigorous proofs. Additionally, we introduce a Network Vulnerability Score (NVS) that leverages these indices to quantify network susceptibility under uncertainty. Comparative analysis reveals that the cubic fuzzy framework offers superior expressiveness for network vulnerability assessment compared to classical fuzzy graphs and intuitionistic fuzzy soft sets
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References
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