{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T23:04:20Z","timestamp":1770419060937,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince Sattam bin Abdulaziz University","award":["PSAU\/2023\/R\/1444"],"award-info":[{"award-number":["PSAU\/2023\/R\/1444"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines. We explain the basic applications of distance-based entropy to chemical phenomena. These applications include signal processing, structural studies on crystals, molecular ensembles, and quantifying the chemical and electrical structures of molecules. In this study, we examine the characterisation of polyphenylenes and boron (B12) using a line of symmetry. Our ability to quickly ascertain the valences of each atom, and the total number of atom bonds is made possible by the symmetrical chemical structures of polyphenylenes and boron B12. By constructing these structures with degree-based indices, namely the K Banhatti indices, ReZG1-index, ReZG2-index, and ReZG3-index, we are able to determine their respective entropies.<\/jats:p>","DOI":"10.3390\/sym15010143","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T01:42:44Z","timestamp":1672796564000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Characterizations of Chemical Networks Entropies by K-Banhatii Topological Indices"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9916-2031","authenticated-orcid":false,"given":"Muhammad Usman","family":"Ghani","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Abu Dhabi Road, Rahim Yar Khan 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6037-6769","authenticated-orcid":false,"given":"Francis Joseph H.","family":"Campena","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, De La Salle University, 2401 Taft Avenue, Malate, Manila 1004, Metro Manila, Philippines"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5998-0053","authenticated-orcid":false,"given":"Shahbaz","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University Bahawalpur Rahim Yar Khan Campus, Rahim Yar Khan 64200, Pakistan"}]},{"given":"Sanaullah","family":"Dehraj","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics Quaid-e-Awam University of Engineering, Science and Technology, Sakrand Road, Nawabshah 67480, Sindh, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8606-2274","authenticated-orcid":false,"given":"Murat","family":"Cancan","sequence":"additional","affiliation":[{"name":"Faculty of Education, Yuzuncu Yil University, Van 65090, Turkey"}]},{"given":"Fahad M.","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3541-9704","authenticated-orcid":false,"given":"Ahmed M.","family":"Galal","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam bin Abdulaziz University, Saudi Arabia"},{"name":"Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, Mansoura P.O. Box 35516, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Tag El Din, E.S.M., Sultan, F., Ghani, M.U., Liu, J.-B., Dehraj, S., Cancan, M., Alharbi, F.M., and Alhushaybari, A. (2022). Some Novel Results Involving Prototypical Computation of Zagreb Polynomials and Indices for SiO 4 Embedded in a Chain of Silicates. Molecules, 28.","DOI":"10.3390\/molecules28010201"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chu, Y.M., Khan, A.R., Ghani, M.U., Ghaffar, A., and Inc, M. (2022). Computation of Zagreb Polynomials and Zagreb Indices for Benzenoid Triangular & Hourglass System. Polycycl. Aromat. 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