{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:38:54Z","timestamp":1740155934014,"version":"3.37.3"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"University Grant Commission, New Delhi","award":["Senior Research Fellowship Award Letter No. F.17-37\/2008(SA-I)"],"award-info":[{"award-number":["Senior Research Fellowship Award Letter No. F.17-37\/2008(SA-I)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p> In this paper, we study the non-commuting graph [Formula: see text] of strictly upper triangular [Formula: see text] matrices over an [Formula: see text]-element chain [Formula: see text]. We prove that [Formula: see text] is a compact graph. From [Formula: see text], we construct a poset [Formula: see text]. We further prove that [Formula: see text] is a dismantlable lattice and its zero-divisor graph is isomorphic to [Formula: see text]. Lastly, we prove that [Formula: see text] is a perfect graph. <\/jats:p>","DOI":"10.1142\/s1793830917500495","type":"journal-article","created":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T04:25:50Z","timestamp":1499055950000},"page":"1750049","source":"Crossref","is-referenced-by-count":0,"title":["Perfect non-commuting graphs of matrices over chains"],"prefix":"10.1142","volume":"09","author":[{"given":"Sarika","family":"Devhare","sequence":"first","affiliation":[{"name":"Center for Advanced Study, Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9105-4634","authenticated-orcid":false,"given":"Vinayak","family":"Joshi","sequence":"additional","affiliation":[{"name":"Center for Advanced Study, Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India"}]}],"member":"219","published-online":{"date-parts":[[2017,8,16]]},"reference":[{"key":"S1793830917500495BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02276109"},{"key":"S1793830917500495BIB002","unstructured":"C. Berge,  \u201cPerfect graphs\u201d: Six Papers on Graph Theory  (Indian Statistical Institute,  Calcutta,  1963),  pp. 1\u201321."},{"key":"S1793830917500495BIB003","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2006.164.51"},{"key":"S1793830917500495BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11083-011-9216-2"},{"issue":"4","key":"S1793830917500495BIB005","first-page":"20","volume":"8","author":"Joshi V.","year":"2016","journal-title":"Discrete Math. Algorithms Appl."},{"key":"S1793830917500495BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(72)90006-4"},{"key":"S1793830917500495BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-010-0955-4"},{"key":"S1793830917500495BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1952-0050559-1"},{"key":"S1793830917500495BIB009","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700019303"},{"key":"S1793830917500495BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2016.11.027"},{"key":"S1793830917500495BIB011","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1974-016-3"},{"key":"S1793830917500495BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(03)00550-0"},{"key":"S1793830917500495BIB013","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2002","edition":"2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500495","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:03:14Z","timestamp":1565096594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500495"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2017,8,16]]},"published-print":{"date-parts":[[2017,8]]}},"alternative-id":["10.1142\/S1793830917500495"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500495","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2017,8]]}}}