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@article{197112,
        author = {Dr.S.SURESH and Ms.R.YUVAREKHA},
        title = {A Comprehensive Review of Spectral Characterization and Structural Transformations in Pythagorean Fuzzy Graphs},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {12},
        number = {11},
        pages = {6936-6942},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=197112},
        abstract = {Pythagorean fuzzy graphs (PFGs) have emerged as an advanced extension of intuitionistic fuzzy graphs, offering greater flexibility in modeling uncertainty through the squared sum condition of membership and non-membership degrees. In recent years, significant attention has been devoted to the spectral characterization of PFGs, particularly in analysing adjacency and Laplacian matrices under Pythagorean fuzzy environments. Spectral properties such as eigen values, spectral radius, and energy play a crucial role in understanding structural behaviour and stability of uncertain networks. This review systematically examines the theoretical developments in spectral analysis of PFGs, highlighting recent results on eigenvalue bounds, spectral invariants, and matrix representations. Furthermore, the study explores various structural transformations, including graph operations, isomorphisms, homomorphisms, and complement structures within the Pythagorean fuzzy framework. Comparative insights between classical, intuitionistic, and Pythagorean fuzzy graph models are also discussed. Applications in decision-making, social network analysis, engineering systems, and uncertain data modeling are summarised to demonstrate practical relevance. Finally, existing research gaps and potential future directions are identified to encourage further advancements in spectral theory and structural analysis of Pythagorean fuzzy graphs.},
        keywords = {Pythagorean fuzzy graph; Spectral characterization; Eigen values; Laplacian matrix; Structural transformations; Graph operations; Uncertainty modeling; Fuzzy set theory; Network analysis; Decision-making systems.},
        month = {April},
        }