Energy and Laplacian Energy of Graphs under the Bipolar Valued Hesitant Fuzzy FrameworkPandey, Sakshi Dev (Avtor) Ranadive, Abhay S. (Avtor) Samanta, Sovan (Avtor) Mršić, Leo (Avtor) Kalampakas, Antonios (Avtor) fuzzy graphbipolar valued hesitant fuzzy graphSpectrumenergyLaplacian energyBipolar-valued hesitant fuzzy graphs (BVHFGs) provide a suitable framework for representing knowledge in situations characterized by uncertainty, imprecision, and hesitations. Current research shows a lack of studies on energy in contexts involving bipolarity, hesitations, and fuzzy data, motivating us to propose new definitions of energy in this area. In this study, we introduce innovative notions of graph energy and Laplacian energy within the framework of a bipolar valued hesitant fuzzy setting and scrutinize certain characteristics and various types of bounds of these concepts. Additionally, the investigation explores the interplay between the energy and Laplacian energy of BVHFGs. Consequently, a numerical illustration is provided, encompassing the identification of optimal alternatives to elucidate the pragmatic application of the proposed theoretical frameworks within the realm of decision-making. This empirical demonstration underscores the efficacy and relevance of the developed methodology in addressing real-world decision-making challenges.Islamic Azad University20262025-10-01 03:56:30Neznano23751UDK: 51ISSN pri članku: 2821-0131COBISS_ID: 251180547sl© By the Authors.