{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T11:21:36Z","timestamp":1764588096752},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> For a group [Formula: see text] and a subset [Formula: see text] of [Formula: see text] the bi-Cayley graph BCay[Formula: see text] of [Formula: see text] with respect to [Formula: see text] is the bipartite graph with vertex set [Formula: see text] and edge set [Formula: see text]. A bi-Cayley graph BCay[Formula: see text] is called a BCI-graph if for any bi-Cayley graph BCay[Formula: see text], [Formula: see text] implies that [Formula: see text] for some [Formula: see text] and [Formula: see text]. A group [Formula: see text] is called a [Formula: see text]-BCI-group if all bi-Cayley graphs of [Formula: see text] with valency at most [Formula: see text] are BCI-graphs. In this paper, we characterize the [Formula: see text]-BCI dihedral groups for [Formula: see text]. Also, we show that the dihedral group [Formula: see text] ([Formula: see text] is prime) is a [Formula: see text]-BCI-group. <\/jats:p>","DOI":"10.1142\/s1793830920500512","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T13:31:41Z","timestamp":1592227901000},"page":"2050051","source":"Crossref","is-referenced-by-count":2,"title":["Isomorphisms of bi-Cayley graphs on Dihedral groups"],"prefix":"10.1142","volume":"12","author":[{"given":"Majid","family":"Arezoomand","sequence":"first","affiliation":[{"name":"University of Larestan, Larestan, Iran"}]},{"given":"Afshin","family":"Behmaram","sequence":"additional","affiliation":[{"name":"Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran"}]},{"given":"Mohsen","family":"Ghasemi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Urmia University, Urmia 57135, Iran"}]},{"given":"Parivash","family":"Raeighasht","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, University of Tabriz, Tabriz, Iran"}]}],"member":"219","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"S1793830920500512BIB001","doi-asserted-by":"publisher","DOI":"10.37236\/3105"},{"key":"S1793830920500512BIB002","first-page":"1","volume":"201","author":"Arezoomand M.","year":"2015","journal-title":"Acta Math Sin. English Ser."},{"issue":"2","key":"S1793830920500512BIB003","first-page":"35","volume":"5","author":"Arezoomand M.","year":"2018","journal-title":"Alg. Struc. Appl."},{"key":"S1793830920500512BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.11.003"},{"key":"S1793830920500512BIB005","first-page":"313","volume":"86","author":"Jin W.","year":"2011","journal-title":"Util. Math."},{"key":"S1793830920500512BIB006","doi-asserted-by":"publisher","DOI":"10.26493\/1855-3974.302.472"},{"issue":"2","key":"S1793830920500512BIB007","first-page":"11","volume":"8","author":"Koike H.","year":"2019","journal-title":"Int. J. Group Theory"},{"key":"S1793830920500512BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2008.06.001"},{"key":"S1793830920500512BIB009","first-page":"177","volume":"80","author":"Lu Z. P.","year":"2006","journal-title":"Ars. Comb."},{"key":"S1793830920500512BIB010","first-page":"213","volume":"15","author":"Qu H. P.","year":"1997","journal-title":"Austral. J. Combin."},{"key":"S1793830920500512BIB011","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022476321014"},{"key":"S1793830920500512BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BF01304186"},{"key":"S1793830920500512BIB013","first-page":"33","volume":"26","author":"Xu S. L.","year":"2008","journal-title":"J. Guangxi Normal. Univ.: Nat. Sci. Edition."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500512","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T09:55:32Z","timestamp":1597312532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500512"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,15]]},"references-count":13,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["10.1142\/S1793830920500512"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500512","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,6,15]]}}}