{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T12:27:05Z","timestamp":1782908825025,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T00:00:00Z","timestamp":1762387200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University, Saudi Arabia","award":["RGP.2\/372\/45"],"award-info":[{"award-number":["RGP.2\/372\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we study the detour eccentric sum index (DESI) to obtain the Quantitative Structure\u2013Property Relationship (QSPR) for different molecular structures. We establish theoretical bounds for this index and compute its values across fundamental graph families. Through correlation analyses between the physicochemical properties of molecular structures representing anti-malarial and breast cancer drugs, we show the high predictive value of two topological parameters, detour diameter (DD) and detour radius (DR). Specifically, DR shows strong positive correlations with boiling point, enthalpy, and flash point (up to 0.94), while DD is highly correlated with properties such as molar volume, molar refraction, and polarizability (up to 0.97). The DESI was then selected for detailed curvilinear regression modeling and comparison against the established eccentric distance sum index. For anti-malarial drugs, the second-order model yields the best fit. The DESI provides optimal prediction for boiling point, enthalpy, and flash point. In breast cancer drugs, the second-order model is again favored for properties except for melting point, best described by a third-order model. The results highlight how well the index captures subtle structural characteristics.<\/jats:p>","DOI":"10.3390\/sym17111897","type":"journal-article","created":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T17:51:43Z","timestamp":1762451503000},"page":"1897","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Detour Eccentric Sum Index for QSPR Modeling in Molecular Structures"],"prefix":"10.3390","volume":"17","author":[{"given":"Supriya","family":"Rajendran","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Kochi 682024, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Radha Rajamani","family":"Iyer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-5943-1290","authenticated-orcid":false,"given":"Ahmad","family":"Asiri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Applied College at Mahail Aseer, King Khalid University, Asir-Abha 61421, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2226-1845","authenticated-orcid":false,"given":"Kanagasabapathi","family":"Somasundaram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0167-5060(08)70381-9","article-title":"Detour distance in graphs","volume":"55","author":"Chartrand","year":"1993","journal-title":"Ann. Discret. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1021\/ci00047a033","article-title":"Applications of graph theory in chemistry","volume":"25","author":"Balaban","year":"1985","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.1246\/bcsj.44.2332","article-title":"A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons","volume":"44","author":"Hosoya","year":"1971","journal-title":"Bull. Chem. Soc. Jpn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"11829","DOI":"10.3934\/math.2022660","article-title":"Topological indices of novel drugs used in blood cancer treatment and its QSPR modeling","volume":"7","author":"Nasir","year":"2022","journal-title":"AIMS Math."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ghani, M.U., Campena, F.J.H., Ali, S., Dehraj, S., Cancan, M., Alharbi, F.M., and Galal, A.M. (2023). Characterizations of Chemical Networks Entropies by K-Banhatii Topological Indices. Symmetry, 15.","DOI":"10.3390\/sym15010143"},{"key":"ref_6","first-page":"105","article-title":"The Wiener index: Development and applications","volume":"68","year":"1995","journal-title":"Croat. Chem. Acta"},{"key":"ref_7","first-page":"873","article-title":"The detour index","volume":"69","author":"Lukovits","year":"1996","journal-title":"Croat. Chem. Acta"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4180650","DOI":"10.1155\/2017\/4180650","article-title":"Gutman index and detour Gutman index of pseudo-regular graphs","volume":"2017","author":"Kavithaa","year":"2017","journal-title":"J. Appl. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"719","DOI":"10.12732\/ijpam.v87i5.5","article-title":"Detour distance pattern of a graph","volume":"87","author":"Abhishek","year":"2013","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_10","first-page":"77","article-title":"Uniform number of a graph","volume":"15","author":"Elakkyia","year":"2020","journal-title":"Iran. J. Math. Sci. Inform."},{"key":"ref_11","first-page":"59","article-title":"Zagreb indices of the total graphs of graphs","volume":"12","author":"Anandkumar","year":"2016","journal-title":"J. Appl. Sci. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"239","DOI":"10.12732\/ijpam.v112i2.2","article-title":"On the hyper-Zagreb index of some operations on graphs","volume":"112","author":"Anandkumar","year":"2017","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3005","DOI":"10.1007\/s12190-023-01869-5","article-title":"Zagreb connection indices in structure property modelling","volume":"69","author":"Mondal","year":"2023","journal-title":"J. Appl. Math. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2150019","DOI":"10.1142\/S1793830921500191","article-title":"Weighted PI index of tensor product and strong product of graphs","volume":"13","author":"Gopika","year":"2020","journal-title":"Discret. Math. Algorithms Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"92","DOI":"10.47443\/dml.2021.s215","article-title":"Padmakar-Ivan index of some types of perfect graphs","volume":"9","author":"Manju","year":"2022","journal-title":"Discret. Math. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e23981","DOI":"10.1016\/j.heliyon.2024.e23981","article-title":"QSPR analysis of distance-based structural indices for drug compounds in tuberculosis treatment","volume":"10","author":"Arockiaraj","year":"2024","journal-title":"Heliyon"},{"key":"ref_17","first-page":"162","article-title":"Analysis of Distance 2 Topological Models of Alkanes","volume":"13","author":"Boraiah","year":"2022","journal-title":"Biointerface Res. Appl. Chem."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Rasheed, M.W., Mahboob, A., and Hanif, I. (2024). Uses of Degree-Based Topological Indices in QSPR Modeling of Drug Properties. Front. Phys., 12.","DOI":"10.3389\/fphy.2024.1381887"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"371","DOI":"10.2478\/AMNS.2019.2.00032","article-title":"QSPR Analysis of Certain Distance Based Topological Indices","volume":"4","author":"Shirakol","year":"2019","journal-title":"Appl. Math. Nonlinear Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/S0022-247X(02)00373-6","article-title":"Eccentric distance sum: A novel graph invariant for predicting biological and physical properties","volume":"275","author":"Gupta","year":"2002","journal-title":"J. Math. Anal. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1504\/IJCBDD.2014.066540","article-title":"Detour matrix-based adjacent path eccentric distance sum indices for QSAR\/QSPR. Part I: Development and evaluation","volume":"7","author":"Singh","year":"2014","journal-title":"Int. J. Comput. Biol. Drug Des."},{"key":"ref_22","unstructured":"Buckley, F., and Harary, F. (1990). Distance in Graphs, Addison-Wesley."},{"key":"ref_23","first-page":"75","article-title":"Detour distance in graphs","volume":"53","author":"Chartrand","year":"2005","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2707","DOI":"10.1016\/j.camwa.2007.10.018","article-title":"Hamiltonian-connected graphs","volume":"55","author":"Zhao","year":"2008","journal-title":"Comput. Math. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"51","DOI":"10.5614\/ejgta.2017.5.1.6","article-title":"The eccentric-distance sum of some graphs","volume":"5","author":"Padmapriya","year":"2017","journal-title":"Electron. J. Graph Theory Appl. (EJGTA)"},{"key":"ref_26","unstructured":"Weisstein, E.W. (2025, March 10). Complete bipartite graph. MathWorld\u2014A Wolfram Web Resource, Available online: https:\/\/mathworld.wolfram.com\/CompleteBipartiteGraph.html."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"49","DOI":"10.2298\/AADM160802001E","article-title":"On distances in generalized Sierpi\u0144ski graphs","volume":"12","year":"2018","journal-title":"Appl. Anal. Discret. Math."},{"key":"ref_28","first-page":"DS6","article-title":"A dynamic survey of graph labeling","volume":"18","author":"Gallian","year":"2015","journal-title":"Electron. J. Comb."},{"key":"ref_29","unstructured":"Rajendran, S., Radhakrishnan, B., and Abhishek, K. On topological integer additive set labeled graph. Gruyter Proc. Math., 2024. in press."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1038\/s41541-021-00401-9","article-title":"Molecular interactions between parasite and mosquito during midgut invasion as targets to block malaria transmission","volume":"6","author":"Keleta","year":"2021","journal-title":"npj Vaccines"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3594","DOI":"10.3934\/mbe.2023167","article-title":"A study on anti-malaria drugs using degree-based topological indices through QSPR analysis","volume":"20","author":"Zhang","year":"2023","journal-title":"Math. Biosci. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1897\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T05:12:03Z","timestamp":1762837923000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,6]]},"references-count":31,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111897"],"URL":"https:\/\/doi.org\/10.3390\/sym17111897","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,6]]}}}