{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T11:14:15Z","timestamp":1760181255226,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,2]],"date-time":"2020-12-02T00:00:00Z","timestamp":1606867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part of artificial intelligence are designed for contact tracing, genetic network analysis for uncovering the biological evolution of the virus, understanding the underlying mechanisms of the observed disease dynamics, evaluating mitigation strategies, and predicting the COVID-19 pandemic dynamics. This paper describes mathematical techniques to exploit and understand the progression of the pandemic through a topological characterization of underlying graphs. We have obtained several topological indices for various graphs of biological interest such as pandemic trees, Cayley trees, Christmas trees, and the corona product of Christmas trees and paths. We have also obtained an analytical expression for the thermodynamic entropies of pandemic trees as a function of R0, the reproduction number, and the level of spread, using the nested wreath product groups. Our plots of entropy and logarithms of topological indices of pandemic trees accentuate the underlying severity of COVID-19 over the 1918 Spanish flu pandemic.<\/jats:p>","DOI":"10.3390\/sym12121992","type":"journal-article","created":{"date-parts":[[2020,12,2]],"date-time":"2020-12-02T20:25:49Z","timestamp":1606940749000},"page":"1992","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Topological and Thermodynamic Entropy Measures for COVID-19 Pandemic through Graph Theory"],"prefix":"10.3390","volume":"12","author":[{"given":"G. Kirithiga","family":"Nandini","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Hindustan Institute of Technology and Science, Chennai 603 103, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. Sundara","family":"Rajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603 103, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. Arul","family":"Shantrinal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603 103, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. M.","family":"Rajalaxmi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603 110, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indra","family":"Rajasingh","sequence":"additional","affiliation":[{"name":"School of Advanced Sciences, Vellore Institute of Technology, Chennai 600 127, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krishnan","family":"Balasubramanian","sequence":"additional","affiliation":[{"name":"School of Molecular Sciences, Arizona State University, Tempe, AZ 85287-1604, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e435","DOI":"10.1016\/S2589-7500(20)30142-4","article-title":"Applications of digital technology in COVID-19 pandemic planning and response","volume":"2","author":"Whitelaw","year":"2020","journal-title":"Lancet Digit. 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