{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:41:45Z","timestamp":1740120105402,"version":"3.37.3"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11861066","11531011"],"award-info":[{"award-number":["11861066","11531011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, any bound on the sum and\/or the product of an invariant in a graph [Formula: see text] and the same invariant in the complement [Formula: see text] of [Formula: see text] is called a Nordhaus-Gaddum type inequality or relation. The Nordhaus-Gaddum type inequalities for connectivity have been studied by several authors. For a bipartite graph [Formula: see text] with bipartition ([Formula: see text]), its bipartite complementary graph [Formula: see text] is a bipartite graph with [Formula: see text] and [Formula: see text] and [Formula: see text]. In this paper, we obtain the Nordhaus-Gaddum type inequalities for connectivity of bipartite graphs and its bipartite complementary graphs. Furthermore, we prove that these inequalities are best possible. <\/jats:p>","DOI":"10.1142\/s0129626420400058","type":"journal-article","created":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T07:38:43Z","timestamp":1602574723000},"page":"2040005","source":"Crossref","is-referenced-by-count":1,"title":["The Connectivity of a Bipartite Graph and Its Bipartite Complementary Graph"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1595-9834","authenticated-orcid":false,"given":"Yingzhi","family":"Tian","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaping","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liyun","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,10,12]]},"reference":[{"key":"S0129626420400058BIB001","first-page":"5","volume":"2","author":"Achuthan N.","year":"1990","journal-title":"Australas. J. Combin."},{"key":"S0129626420400058BIB002","first-page":"1","volume-title":"Recent Trends in Graph Theory","author":"Alavi Y.","year":"1970"},{"key":"S0129626420400058BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.12.018"},{"key":"S0129626420400058BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"S0129626420400058BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2008.05.012"},{"key":"S0129626420400058BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01433466"},{"key":"S0129626420400058BIB008","doi-asserted-by":"publisher","DOI":"10.2307\/2306658"},{"key":"S0129626420400058BIB009","unstructured":"M. Y. Xu,  Introduction of Finite Groups,  Vol.\u00a0II  (Science Press,  Beijing,  1999),  pp.\u00a0384\u2013386."}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626420400058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T07:38:49Z","timestamp":1602574729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626420400058"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":8,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1142\/S0129626420400058"],"URL":"https:\/\/doi.org\/10.1142\/s0129626420400058","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"type":"print","value":"0129-6264"},{"type":"electronic","value":"1793-642X"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}