Anitha Saravanakumar, Jayalakshmi Periyannan, Prasantha Bharathi Dhandapani, Nisky Imansyah Yahya
This study extends fuzzy graph energy analysis by introducing energy and Laplacian energy for Pythagorean Intuitionistic Fuzzy Graphs (PIFGs), a powerful generalization of intuitionistic fuzzy graphs capable of representing higher degrees of uncertainty. A novel connection matrix for PIFGs is defined, and new formulations for energy and Laplacian energy are established, along with sharp lower and upper bounds. Beyond theoretical contributions, the approach is applied to medical diagnosis networks, where vertices represent symptoms, diagnostic tests, and diseases, and edges encode Pythagorean intuitionistic fuzzy relationships. These measures quantify both the overall strength of associations (energy) and their structural irregularity (Laplacian energy), offering interpretable indicators for diagnostic certainty or ambiguity. The framework provides a robust mathematical basis for decision-making in biomedical contexts where data are uncertain, imprecise, or conflicting. © 2025 by author(s).
Department of Mathematics, Soka Ikeda College of Arts and Science for Women (Affiliated to University of Madras), Tamil Nadu, Chennai, India; Department of Mathematics, Sri G.V.G. Visalakshi College for Women (Affiliated to Bharathiar University), Tiruppur, TamilNadu, Udumalpet, India; Department of Mathematics, Sri Eshwar College of Engineering, Tamil Nadu, Coimbatore, 641202, India; Department of Mathematics, Universitas Negeri Gorontalo, Bone Bolango, 96554, Indonesia
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