Ghani, Muhammad UsmanCampena, Francis Joseph H.Maqbool, Muhammad KashifLiu, Jia-BaoDehraj, SanaullahCancan, MuratAlharbi, Fahad M.2025-05-102025-05-1020231420-304910.3390/molecules280104522-s2.0-85145678910https://doi.org/10.3390/molecules28010452https://hdl.handle.net/20.500.14720/9973Campena, Francis Joseph/0000-0002-6037-6769; Liu, Jia-Bao/0000-0002-9620-7692Entropy is a measure of a system's molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon's entropy metric is applied to represent a random graph's variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules' chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at K-Banhatti entropies using K-Banhatti indices for C6H6 embedded in different chemical networks. Our goal is to investigate the valency-based molecular invariants and K-Banhatti entropies for three chemical networks: the circumnaphthalene (CNBn), the honeycomb (HBn), and the pyrene (PYn). In order to reach conclusions, we apply the method of atom-bond partitioning based on valences, which is an application of spectral graph theory. We obtain the precise values of the first K-Banhatti entropy, the second K-Banhatti entropy, the first hyper K-Banhatti entropy, and the second hyper K-Banhatti entropy for the three chemical networks in the main results and conclusion.eninfo:eu-repo/semantics/openAccessC6H6 Embedded In Pyrene NetworkC6H6 Embedded In Circumnaphthalene NetworkC6H6 Embedded In Honeycomb NetworkK-Banhatti EntropiesArticle281Q2Q236615642WOS:000911105700001