{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:07:49Z","timestamp":1699834069826},"reference-count":2,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":9355,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1981,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The connectivity contribution or cohesiveness of a point <jats:italic>v<\/jats:italic> of graph <jats:italic>G<\/jats:italic> is defined as the difference <jats:italic>k<\/jats:italic>(<jats:italic>G<\/jats:italic>) \u2010 <jats:italic>k<\/jats:italic>(<jats:italic>G<\/jats:italic> \u2010 <jats:italic>v<\/jats:italic>) where kappa is the usual connectivity symbol. It is shown that if a point <jats:italic>v<\/jats:italic> of <jats:italic>G<\/jats:italic> has negative cohesiveness, then the set of points adjacent to <jats:italic>v<\/jats:italic> is the unique minimum size disconnecting set of <jats:italic>G<\/jats:italic>. This theorem has several corollaries including the result that if <jats:italic>v<\/jats:italic> has negative cohesiveness in <jats:italic>G<\/jats:italic>, then it does not in \u0393. Finally we define a cohesiveness triple (<jats:italic>n_, n<jats:sub>0<\/jats:sub>, n<jats:sub>+<\/jats:sub><\/jats:italic>) of a graph by taking these, respectively, as the number of negative, zero, and positive cohesiveness points of <jats:italic>G<\/jats:italic>. The necessary and sufficient conditions for an arbitrary triple to be the cohesiveness triple of a graph are derived.<\/jats:p>","DOI":"10.1002\/net.3230110107","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T11:46:51Z","timestamp":1178884011000},"page":"65-68","source":"Crossref","is-referenced-by-count":5,"title":["The cohesiveness of a point of a graph"],"prefix":"10.1002","volume":"11","author":[{"given":"Jin","family":"Akiyama","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Boesch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroshi","family":"Era","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Harary","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ralph","family":"Tindell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/bs.3830020403"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230110107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230110107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T12:14:48Z","timestamp":1699791288000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230110107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,3]]},"references-count":2,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1981,3]]}},"alternative-id":["10.1002\/net.3230110107"],"URL":"https:\/\/doi.org\/10.1002\/net.3230110107","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1981,3]]}}}