{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T22:07:12Z","timestamp":1698358032808},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7611,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The distance of a vertex <jats:italic>u<\/jats:italic> in a connected graph <jats:italic>H<\/jats:italic> is the sum of all the distances from <jats:italic>u<\/jats:italic> to the other vertices of <jats:italic>H.<\/jats:italic> The median <jats:italic>M(H)<\/jats:italic> of <jats:italic>H<\/jats:italic> is the subgraph of <jats:italic>H<\/jats:italic> induced by the vertices of minimum distance. For any graph <jats:italic>G<\/jats:italic>, let <jats:italic>f(G)<\/jats:italic> denote the minimum order of a connected graph <jats:italic>H<\/jats:italic> satisfying <jats:italic>M(H)<\/jats:italic> \u2245 <jats:italic>G.<\/jats:italic> It is shown that if <jats:italic>G<\/jats:italic> has <jats:italic>n<\/jats:italic> vertices and minimum degree \u03b4 then <jats:italic>f(G)<\/jats:italic> \u2a7d 2<jats:italic>n<\/jats:italic> \u2212 \u03b4 + 1. Graphs having both median and center prescribed are constructed. It is also shown that if the vertices of a <jats:italic>K<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub> are removed from a graph <jats:italic>H<\/jats:italic>, then at most <jats:italic>r<\/jats:italic> components of the resulting graph contain median vertices of <jats:italic>H<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/jgt.3190090407","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:55:28Z","timestamp":1180425328000},"page":"477-481","source":"Crossref","is-referenced-by-count":9,"title":["On graphs with prescribed median I"],"prefix":"10.1002","volume":"9","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","volume-title":"Graphs and Digraphs","author":"Behzad M.","year":"1979"},{"key":"e_1_2_1_3_2","unstructured":"F.Buckley self\u2010centered graphs with a given radius. In Proceedings Tenth Southeastern Conference on Combinatorics Graph Theory and Computing F. Hoffman Ed. Utilitas Math. Winnipeg (1979) pp.211\u2013215."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90164-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050413"},{"key":"e_1_2_1_6_2","unstructured":"G. R. T.Hendry On graphs with prescribed median II. Forthcoming."},{"key":"e_1_2_1_7_2","first-page":"226","article-title":"Centers and radii of graphs","volume":"32","author":"Kopylov G. N.","year":"1977","journal-title":"Uspehi Mat. Nauk."},{"key":"e_1_2_1_8_2","first-page":"169","article-title":"Medians and distance sequences in graphs","volume":"15","author":"Miller Z.","year":"1983","journal-title":"Ars Combinatoria"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190040408"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190090407","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T23:24:10Z","timestamp":1697757850000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190090407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,12]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1985,12]]}},"alternative-id":["10.1002\/jgt.3190090407"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190090407","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,12]]}}}