{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T15:24:55Z","timestamp":1759937095842,"version":"3.33.0"},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7702,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let<jats:italic>d<\/jats:italic><jats:sub>i<\/jats:sub>the degree of the<jats:italic>i<\/jats:italic>th vertex of a mutigraph and \u03bb<jats:sub>ij<\/jats:sub>be the number of edges between vertex<jats:italic>i<\/jats:italic>and vertex<jats:italic>j.<\/jats:italic>A multigraph is called nearly balanced if |<jats:italic>d<\/jats:italic><jats:sub>i<\/jats:sub>\u2212<jats:italic>d<\/jats:italic><jats:sub>i<\/jats:sub>| \u22641 for all<jats:italic>i<\/jats:italic>\u2260<jats:italic>i<\/jats:italic>\u2032 and |\u03bb<jats:sub>ij<\/jats:sub>\u2212\u03bb<jats:sub>ij<\/jats:sub>| for all<jats:italic>i<\/jats:italic>and all<jats:italic>j<\/jats:italic>,<jats:italic>j<\/jats:italic>\u2032 Let be the collection of all the multigraphs with<jats:italic>v<\/jats:italic>vertices and e edges. It is shown that for any<jats:italic>v<\/jats:italic>, there is an<jats:italic>e<\/jats:italic>* such that if, then any nearly balanced graph in \u03b6<jats:sub>v, e<\/jats:sub>has more spanning trees than any non\u2010nearly\u2010balanced graph in \u03b6<jats:sub>v, e<\/jats:sub>.<\/jats:p>","DOI":"10.1002\/jgt.3190090306","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:16:36Z","timestamp":1180422996000},"page":"342-345","source":"Crossref","is-referenced-by-count":5,"title":["Do nearly balanced multigraphs have more spanning trees?"],"prefix":"10.1002","volume":"9","author":[{"given":"Ching\u2010Shui","family":"Cheng","sequence":"first","affiliation":[]},{"given":"Joseph C.","family":"Masaro","sequence":"additional","affiliation":[]},{"given":"Chi Song","family":"Wong","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608704"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(81)80028-7"},{"key":"e_1_2_1_4_2","first-page":"264","article-title":"Graphs with prescribed degrees of vertices","volume":"11","author":"Erd\u00f6s P.","year":"1960","journal-title":"Math. Lapok"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1111\/j.2517-6161.1977.tb01602.x","article-title":"Optimal incomplete block designs","volume":"39","author":"John J. A.","year":"1977","journal-title":"J. R. Stat. Soc. B"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90065-3"},{"volume-title":"Inequalities: Theory of Majorization and its Applications","year":"1979","author":"Marshall A. W.","key":"e_1_2_1_7_2"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.078B.023"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190090306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090306","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T18:50:18Z","timestamp":1737053418000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190090306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1985,9]]}},"alternative-id":["10.1002\/jgt.3190090306"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190090306","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"type":"print","value":"0364-9024"},{"type":"electronic","value":"1097-0118"}],"subject":[],"published":{"date-parts":[[1985,9]]}}}