{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T07:04:40Z","timestamp":1723100680192},"reference-count":11,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2004,1,30]],"date-time":"2004-01-30T00:00:00Z","timestamp":1075420800000},"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":[[2004,4]]},"abstract":"Abstract<\/jats:title>For any graph G<\/jats:italic>, let ni<\/jats:sub><\/jats:italic> be the number of vertices of degree i<\/jats:italic>, and $\\lambda (G)={max} _{i\\le j}\\{ {n_i+\\cdots +n_j+i-1\\over j}\\}$<\/jats:styled-content>. This is a general lower bound on the irregularity strength of graph G<\/jats:italic>. All known facts suggest that for connected graphs, this is the actual irregularity strength up to an additive constant. In fact, this was conjectured to be the truth for regular graphs and for trees. Here we find an infinite sequence of trees with \u03bb(T<\/jats:italic>)\u2009=\u2009n<\/jats:italic>1<\/jats:sub> but strength converging to ${11-\\sqrt 5\\over 8} n_1$<\/jats:styled-content>. \u00a9 2004 Wiley Periodicals, Inc. J Graph Theory 45: 241\u2013254, 2004<\/jats:p>","DOI":"10.1002\/jgt.10158","type":"journal-article","created":{"date-parts":[[2004,2,16]],"date-time":"2004-02-16T08:13:23Z","timestamp":1076919203000},"page":"241-254","source":"Crossref","is-referenced-by-count":58,"title":["On the irregularity strength of trees"],"prefix":"10.1002","volume":"45","author":[{"given":"Tom","family":"Bohman","sequence":"first","affiliation":[]},{"given":"David","family":"Kravitz","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,2,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00112-5"},{"key":"e_1_2_1_3_2","first-page":"187","article-title":"Irregular networks","volume":"64","author":"Chartrand G.","year":"1988","journal-title":"Congress Numerantium"},{"key":"e_1_2_1_4_2","first-page":"113","article-title":"Irregularity strength of full d\u2010ary trees","volume":"81","author":"Cammack L. A.","year":"1991","journal-title":"Congressus Numerantium"},{"key":"e_1_2_1_5_2","first-page":"39","article-title":"Irregularity strengths for certain graphs","volume":"71","author":"Ebert G.","year":"1990","journal-title":"Congressus Numerantium"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10056"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(89)90321-X"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(80)90042-8"},{"key":"e_1_2_1_9_2","unstructured":"M. S.JacobsonandJ.Lehel A bound for the strength of an irregular network Dept. of Math. University of Louisville (The revised version Upper bound on the irregularity strength of a simple graph has never been published) 1986 pp23."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90309-P"},{"key":"e_1_2_1_11_2","unstructured":"D.Kravitz Investigation of the irregularity strength of trees Undergraduate thesis University of Delaware 2000."},{"key":"e_1_2_1_12_2","unstructured":"J.Lehel Facts and quests on degree irregular assignments Sixth International Conference on Graph Theory Combinatorics and Applications (Kalamazoo MI 1988) Vol. 2 Wiley\u2010Interscience Publications Wiley New York 1991. pp765\u2013782."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.10158","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.10158","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T00:15:50Z","timestamp":1697674550000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.10158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,13]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,4]]}},"alternative-id":["10.1002\/jgt.10158"],"URL":"https:\/\/doi.org\/10.1002\/jgt.10158","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,13]]}}}