{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T00:16:32Z","timestamp":1773360992390,"version":"3.50.1"},"reference-count":8,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":6280,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1989,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The mean distance of a simple connected graph <jats:italic>G<\/jats:italic> of order <jats:italic>n<\/jats:italic> is defined by <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> We answer a problem of Plesnik about the edge\u2010vulnerability of <jats:italic>G<\/jats:italic> related to \u03bc, i.e., we find a bound for \u03bc(<jats:italic>G<\/jats:italic> \u2212 <jats:italic>e<\/jats:italic>) \u2212 \u03bc(<jats:italic>G<\/jats:italic>) and for <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must002.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> where <jats:italic>e<\/jats:italic> is an edge of <jats:italic>G<\/jats:italic> such that <jats:italic>G<\/jats:italic> \u2212 <jats:italic>e<\/jats:italic> is still conencted. This question is of interest in interconnection La distance moyenne d'un graphe <jats:italic>G<\/jats:italic>, simple et connexe, d'ordre <jats:italic>n<\/jats:italic>, est d\u00e9finie par <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> Nous r\u00e9pondons ici \u00e0 un probl\u00e8me de Plesnik sur l'ar\u011bte\u2010vuln\u00e9rabilit\u00e9 de G par rapport \u00e0 \u03bc, i.e. nous trouvons une borne pour \u03bc(<jats:italic>G \u2212e<\/jats:italic>) \u2212 \u03bc(<jats:italic>G<\/jats:italic>) et pour <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must002.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> o\u00fa <jats:italic>e<\/jats:italic> est une ar\u011bte de <jats:italic>G<\/jats:italic> telle que <jats:italic>G<\/jats:italic> \u2212 <jats:italic>e<\/jats:italic> soit encore connexe.<\/jats:p>","DOI":"10.1002\/net.3230190502","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T03:16:45Z","timestamp":1178939805000},"page":"493-504","source":"Crossref","is-referenced-by-count":21,"title":["Edge\u2010vulnerability and mean distance"],"prefix":"10.1002","volume":"19","author":[{"given":"Odile","family":"Favaron","sequence":"first","affiliation":[]},{"given":"Mekkia","family":"Kouider","sequence":"additional","affiliation":[]},{"given":"Maryvonne","family":"Mah\u00e9o","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120309"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190080408"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1980.1084857"},{"key":"e_1_2_1_5_2","unstructured":"M.Kouider On one four\u2010thirds conjecture Preprint."},{"key":"e_1_2_1_6_2","first-page":"455","volume-title":"Note on Diametrically Critically Graphs, Recent Advances in Graph Theory (Proc. Symp. Prague 1974)","author":"Plesnik J."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190080102"},{"key":"e_1_2_1_8_2","unstructured":"P.Winkler Problems from the conference in Sandbjerg (Denmark) June1985."},{"key":"e_1_2_1_9_2","first-page":"53","article-title":"Mean distance and the \u201cfour\u2010thirds conjecture\u201d","volume":"54","author":"Winkler P.","year":"1986","journal-title":"Congressus Numerantium"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230190502","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230190502","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T08:43:34Z","timestamp":1697964214000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230190502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,8]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1989,8]]}},"alternative-id":["10.1002\/net.3230190502"],"URL":"https:\/\/doi.org\/10.1002\/net.3230190502","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,8]]}}}