Advanced bounds for eigenvalues in spectral fuzzy graph theory

Document Type : Research Article

Authors

1 Assistant Professor, Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamil Nadu, India

2 Assistant Professor, Faculty of Mathematics, Dr.Mahalingam College of Engineering and Technology, Coimbatore, Tamil Nadu, India

3 Department of Applied Mathematics,Ayandegan Institute of Higher Education,Tonekabon,Iran and Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India

Abstract

This paper introduces advanced eigenvalue bounds for Spectral Fuzzy Graphs (SFGs), a subclass of fuzzy graphs with symmetric adjacency matrices enhancing the precision of spectral graph analysis. Leveraging the Rayleigh quotient and the Perron-Frobenius theorem, we establish novel upper and lower bounds for the largest and smallest eigenvalues of fuzzy adjacency matrices. Specific results include eigenvalue bounds for complete and bipartite fuzzy graphs, as well as the demonstration of eigenvalue stability under graph perturbations and unions. A numerical example based on a protein interaction network illustrates the practical applicability of the proposed methods, demonstrating improved accuracy in analyzing network resilience and connectivity.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 1
March 2026
Pages 137-160

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