{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:21:31Z","timestamp":1753881691588,"version":"3.41.2"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"national natural science foundation of china","doi-asserted-by":"publisher","award":["11661066"],"award-info":[{"award-number":["11661066"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p> For a given graph [Formula: see text], by [Formula: see text] and [Formula: see text] denote the order of the largest component and the number of connected components of [Formula: see text], respectively. The rupture degree of [Formula: see text] is an important combinatorial parameters, which defined as [Formula: see text]. Clearly, the smaller the value [Formula: see text] is, the better the connectivity of graph [Formula: see text] is. In this paper, the tree structures with minimum rupture degree be discussed, and the extremal graphs on the rupture degree in terms of graph girth are also characterized. <\/jats:p>","DOI":"10.1142\/s0219265921420123","type":"journal-article","created":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T07:01:22Z","timestamp":1627628482000},"source":"Crossref","is-referenced-by-count":0,"title":["Extremal Graphs on the Rupture Degree"],"prefix":"10.1142","volume":"21","author":[{"given":"Xiaoxiao","family":"Qin","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810000, P. R. 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