{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T18:06:44Z","timestamp":1770228404245,"version":"3.49.0"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p> The permutability graph of subgroups of a given group G, denoted by \u0393(G), is a graph with vertex set consists of all the proper subgroups of G and two distinct vertices in \u0393(G) are adjacent if and only if the corresponding subgroups permute in G. In this paper, we classify the finite groups whose permutability graphs of subgroups are one of bipartite, star graph, C<jats:sub>3<\/jats:sub>-free, C<jats:sub>5<\/jats:sub>-free, K<jats:sub>4<\/jats:sub>-free, K<jats:sub>5<\/jats:sub>-free, K<jats:sub>1,4<\/jats:sub>-free, K<jats:sub>2,3<\/jats:sub>-free or P<jats:sub>n<\/jats:sub>-free (n = 2, 3, 4). We investigate the same for infinite groups also. Moreover, some results on the girth, completeness and regularity of the permutability graphs of subgroups of groups are obtained. Among the other results, we characterize groups Q<jats:sub>8<\/jats:sub>, S<jats:sub>3<\/jats:sub> and A<jats:sub>4<\/jats:sub> by using their permutability graphs of subgroups. <\/jats:p>","DOI":"10.1142\/s1793830915500123","type":"journal-article","created":{"date-parts":[[2015,2,6]],"date-time":"2015-02-06T01:28:58Z","timestamp":1423186138000},"page":"1550012","source":"Crossref","is-referenced-by-count":6,"title":["On permutability graphs of subgroups of groups"],"prefix":"10.1142","volume":"07","author":[{"given":"R.","family":"Rajkumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamil Nadu, India"}]},{"given":"P.","family":"Devi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2015,5,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1080\/00927870701302081"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s10231-009-0124-7"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/22.6.569"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01759356"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010362602070"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-006-7392-8"},{"key":"rf7","volume-title":"Theory of Groups of Finite Order","author":"Burnside W.","year":"1955"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01759389"},{"key":"rf9","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"key":"rf10","first-page":"171","volume":"4","author":"Iwasawa K.","year":"1941","journal-title":"J. Fac. Sci. Imp. Univ. Tokyo Sect. I"},{"key":"rf11","first-page":"167","volume":"5","author":"Lin H. L.","year":"1974","journal-title":"Tamkang J. Math."},{"key":"rf12","first-page":"309","author":"Ol'shanskii A. Yu.","year":"1980","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498813501120"},{"key":"rf14","volume-title":"Group Theory","author":"Scott W. R.","year":"1964"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:35:55Z","timestamp":1565148955000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,25]]},"references-count":14,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2015,5,25]]},"published-print":{"date-parts":[[2015,6]]}},"alternative-id":["10.1142\/S1793830915500123"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500123","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,25]]}}}