{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:56:17Z","timestamp":1758272177810},"reference-count":6,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4782,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The directed distance <jats:italic>d<\/jats:italic><jats:sub><jats:italic>D<\/jats:italic><\/jats:sub>(<jats:italic>u, v<\/jats:italic>) from a vertex <jats:italic>u<\/jats:italic> to a vertex <jats:italic>v<\/jats:italic> in a strong digraph <jats:italic>D<\/jats:italic> is the length of a shortest (directed) <jats:italic>u \u2010 v<\/jats:italic> path in <jats:italic>D.<\/jats:italic> The eccentricity of a vertex <jats:italic>v<\/jats:italic> in <jats:italic>D<\/jats:italic> is the directed distance from <jats:italic>v<\/jats:italic> to a vertex furthest from <jats:italic>v.<\/jats:italic> The distance of a vertex <jats:italic>v<\/jats:italic> in <jats:italic>D<\/jats:italic> is the sum of the directed distances from <jats:italic>v<\/jats:italic> to the vertices of <jats:italic>D.<\/jats:italic> The center <jats:italic>C<\/jats:italic>(<jats:italic>D<\/jats:italic>) of <jats:italic>D<\/jats:italic> is the subdigraph induced by those vertices of minimum eccentricity, while the median <jats:italic>M<\/jats:italic>(<jats:italic>D<\/jats:italic>) of <jats:italic>D<\/jats:italic> is the subdigraph induced by those vertices of minimum distance. It is shown that for every two asymmetric digraphs <jats:italic>D<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>D<\/jats:italic><jats:sub>2<\/jats:sub>, there exists a strong asymmetric digraph <jats:italic>H<\/jats:italic> such that <jats:italic>C<\/jats:italic>(<jats:italic>H<\/jats:italic>) \u2245 <jats:italic>D<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>M<\/jats:italic>(<jats:italic>H<\/jats:italic>) \u2245 <jats:italic>D<\/jats:italic><jats:sub>2<\/jats:sub>, and where the directed distance from <jats:italic>C<\/jats:italic>(<jats:italic>H<\/jats:italic>) to <jats:italic>M<\/jats:italic>(<jats:italic>H<\/jats:italic>) and from <jats:italic>M<\/jats:italic>(<jats:italic>H<\/jats:italic>) to <jats:italic>C<\/jats:italic>(<jats:italic>H<\/jats:italic>) can be arbitrarily prescribed. Furthermore, if <jats:italic>K<\/jats:italic> is a nonempty asymmetric digraph isomorphic to an induced subdigraph of both <jats:italic>D<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>D<\/jats:italic><jats:sub>2<\/jats:sub>, then there exists a strong asymmetric digraph <jats:italic>F<\/jats:italic> such that <jats:italic>C<\/jats:italic>(<jats:italic>F<\/jats:italic>) \u2245 <jats:italic>D<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>M<\/jats:italic>(<jats:italic>F<\/jats:italic>) \u2245 <jats:italic>D<\/jats:italic><jats:sub>2<\/jats:sub> and <jats:italic>C<\/jats:italic>(<jats:italic>F<\/jats:italic>) \u2229 <jats:italic>M<\/jats:italic>(<jats:italic>F<\/jats:italic>) \u2245 <jats:italic>K.<\/jats:italic> \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170408","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:24:17Z","timestamp":1181240657000},"page":"509-521","source":"Crossref","is-referenced-by-count":5,"title":["Directed distance in digraphs: Centers and medians"],"prefix":"10.1002","volume":"17","author":[{"given":"Gary","family":"Chartrand","sequence":"first","affiliation":[]},{"given":"Garry L.","family":"Johns","sequence":"additional","affiliation":[]},{"given":"Songlin","family":"Tian","sequence":"additional","affiliation":[]},{"given":"Steven J.","family":"Winters","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Distance in Graphs","author":"Buckley F.","year":"1990"},{"key":"e_1_2_1_3_2","unstructured":"G.Chartrand G. L.Johns andS.Tian Directed distance in digraphs: Centers and peripheries.Congress. Numer.To appear."},{"key":"e_1_2_1_4_2","unstructured":"G.ChartrandandS.Tian Distance in digraphs.Mathematics and Computer Models. To appear."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090407"},{"key":"e_1_2_1_6_2","first-page":"155","volume-title":"Recent Studies in Graph Theory","author":"Holbert K. S.","year":"1989"},{"key":"e_1_2_1_7_2","first-page":"297","volume-title":"Advances in Graph Theory","author":"Novotny K.","year":"1991"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170408","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170408","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T03:21:28Z","timestamp":1698204088000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["10.1002\/jgt.3190170408"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170408","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}