{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T05:01:06Z","timestamp":1698037266991},"reference-count":6,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T00:00:00Z","timestamp":1159920000000},"content-version":"vor","delay-in-days":6973,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1987,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The hamiltonian path graph <jats:italic>H(F)<\/jats:italic> of a graph <jats:italic>F<\/jats:italic> is that graph having the same vertex set as <jats:italic>F<\/jats:italic> and in which two vertices u and <jats:italic>v<\/jats:italic> are adjacent if and only if <jats:italic>F<\/jats:italic> contains a hamiltonian u \u2212 <jats:italic>v<\/jats:italic> path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian graphs isomorphic to their hamiltonian path graphs is presented. Next, the maximum size of a hamiltonian graph <jats:italic>F<\/jats:italic> of given order such that <jats:italic>K\u0304<jats:sub>d<\/jats:sub> \u2286 H(F)<\/jats:italic> is determined. Finally, it is shown that if the degree sum of the endvertices of a hamiltonian path in a graph <jats:italic>F<\/jats:italic> with at least five vertices is at least |<jats:italic>V(F)<\/jats:italic>| + <jats:italic>t(t<\/jats:italic> \u2a7e 0), then <jats:italic>H(F)<\/jats:italic> contains a complete subgraph of order <jats:italic>t<\/jats:italic> + 4.<\/jats:p>","DOI":"10.1002\/jgt.3190110312","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T04:11:17Z","timestamp":1181362277000},"page":"373-384","source":"Crossref","is-referenced-by-count":4,"title":["On the hamiltonian path graph of a graph"],"prefix":"10.1002","volume":"11","author":[{"given":"George R. T.","family":"Hendry","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,4]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Digraphs","author":"Behzad M.","year":"1979"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070406"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"e_1_2_1_5_2","unstructured":"G. R. T.Hendry On paths factors and cycles in graphs. Ph.D. Thesis Aberdeen University (1985)."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(80)90042-8"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90038-5"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190110312","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190110312","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:28:31Z","timestamp":1697999311000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190110312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1987,9]]}},"alternative-id":["10.1002\/jgt.3190110312"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190110312","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,9]]}}}