{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T21:10:57Z","timestamp":1698009057836},"reference-count":3,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7429,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1986,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is shown that for each rational number <jats:italic>t<\/jats:italic> \u2265 1 there exist infinitely many graphs with mean distance equal to <jats:italic>t<\/jats:italic>.<\/jats:p><jats:p>For a graph <jats:italic>G<\/jats:italic>, define the <jats:italic>mean distance<\/jats:italic> \u03bc(<jats:italic>G<\/jats:italic>) by <jats:disp-formula>\n\n<\/jats:disp-formula>.<\/jats:p><jats:p>In an earlier issue of this journal, J. Plesn\u00edk [3, Theorem 9] showed that, given real numbers <jats:italic>t<\/jats:italic> \u2265 1 and \u03f5 &gt; 0, there exists a graph <jats:italic>G<\/jats:italic> with |\u03bc(<jats:italic>G<\/jats:italic>)\u2212<jats:italic>t<\/jats:italic>| &lt; \u03f5. Furthermore, he asked [3, p. 19]: Given a rational number <jats:italic>t<\/jats:italic> \u2265 1, does there exist a graph <jats:italic>G<\/jats:italic> with \u03bc(<jats:italic>G<\/jats:italic>) = <jats:italic>t<\/jats:italic>? We answer this question in the affirmative by proving:<\/jats:p>","DOI":"10.1002\/jgt.3190100205","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:56:27Z","timestamp":1180180587000},"page":"173-175","source":"Crossref","is-referenced-by-count":4,"title":["Existence of graphs with prescribed mean distance"],"prefix":"10.1002","volume":"10","author":[{"given":"G. R. T.","family":"Hendry","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90144-3"},{"key":"e_1_2_1_3_2","unstructured":"G. R. T.Hendry On mean distance in certain classes of graphs in preparation."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190080102"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190100205","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190100205","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T22:53:22Z","timestamp":1697928802000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190100205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,6]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1986,6]]}},"alternative-id":["10.1002\/jgt.3190100205"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190100205","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,6]]}}}