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Determining whether a graph is Hamilton\u2010connected is an NP\u2010complete problem. Hamiltonian and Hamilton\u2010connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP\u2010complete problem. In this paper, we study the Hamilton\u2010connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton\u2010connected. An infinite family of non\u2010Hamilton\u2010connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton\u2010connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.<\/jats:p>","DOI":"10.1155\/2021\/6684784","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T20:07:03Z","timestamp":1611605223000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5100-6259","authenticated-orcid":false,"given":"Sakander","family":"Hayat","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1261-0418","authenticated-orcid":false,"given":"Asad","family":"Khan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3566-9145","authenticated-orcid":false,"given":"Suliman","family":"Khan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9620-7692","authenticated-orcid":false,"given":"Jia-Bao","family":"Liu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"key":"e_1_2_11_1_2","first-page":"21","article-title":"Hamilton-connected graphs","volume":"42","author":"Ore O.","year":"1963","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010111"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.11.040"},{"key":"e_1_2_11_4_2","first-page":"104","article-title":"The Hamiltonicity of generalized honeycomb torus networks","volume":"115","author":"Qiang S.","year":"2005","journal-title":"Information Processing Letters"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2016.10.015"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365x(93)90555-8"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2004.05.017"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90075-6"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(80)90061-1"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.20039"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2007.10.018"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2016.1182463"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.03.063"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.08.005"},{"key":"e_1_2_11_15_2","first-page":"1","article-title":"The Hamiltonian connectivity of alphabet supergrid graphs","volume":"49","author":"Hung R. 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