{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T04:46:54Z","timestamp":1697690814601},"reference-count":13,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T00:00:00Z","timestamp":1172102400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2007,8]]},"abstract":"Abstract<\/jats:title>We prove new isoperimetric inequalities on graphs involving quantities linked with concepts from differential geometry. First, we bound from above the product of the volume entropy (defined as the log of the exponential growth rate of the universal cover) and the girth of weighted graphs in terms of their cyclomatic number. In a second part, we study a natural polyhedron associated to a weighted graph: the stable ball. In particular, we relate the volume of this polyhedron, the weight of the graph and its cyclomatic number. \u00a9 2007 Wiley Periodicals, Inc. J Graph Theory 55: 291\u2013305, 2007<\/jats:p>","DOI":"10.1002\/jgt.20236","type":"journal-article","created":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T20:40:41Z","timestamp":1172176841000},"page":"291-305","source":"Crossref","is-referenced-by-count":1,"title":["Volume entropy, weighted girths and stable balls on graphs"],"prefix":"10.1002","volume":"55","author":[{"given":"Florent","family":"Balacheff","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,2,22]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-005-0668-9"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-005-0622-x"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","DOI":"10.1090\/cbms\/062","article-title":"Extremal graph theory with emphasis on probabilistic methods","volume":"62","author":"Bollob\u00e1s B.","year":"1986","journal-title":"CBMS Regional Conference Series in Mathematics"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10023"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01232233"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214509283"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021273024728"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385704001014"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/1971239"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(88)90068-7"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1017\/S014338570600006X"},{"key":"e_1_2_1_13_2","volume-title":"Algebraic topology","author":"Spanier E.","year":"1995"},{"key":"e_1_2_1_14_2","first-page":"32","article-title":"A volume invariant of coverings","volume":"105","author":"Sv\u0301arc A.","year":"1955","journal-title":"Dokl Ak Nauk SSSR"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20236","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T10:53:15Z","timestamp":1697626395000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,22]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,8]]}},"alternative-id":["10.1002\/jgt.20236"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20236","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,22]]}}}