{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T04:42:45Z","timestamp":1698468165928},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p>Let (P, \u2264) be a partially ordered set (poset, briefly) with a least element 0. The intersection graph of ideal of P, denoted by G(P), is a graph whose vertices are all non-trivial ideals of P and two distinct vertices I and J are adjacent if and only if I \u2229 J \u2260 {0}. In this paper, we study some relations between the algebraic properties of posets and graph-theoretic properties of G(P). We investigate the connectivity, diameter, girth and planarity of the intersection graph. Also, among the other things, we show that if the clique number of G(P) is finite, then P is finite too.<\/jats:p>","DOI":"10.1142\/s1793830914500360","type":"journal-article","created":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T03:54:43Z","timestamp":1394596483000},"page":"1450036","source":"Crossref","is-referenced-by-count":1,"title":["The intersection graph of ideals of a poset"],"prefix":"10.1142","volume":"06","author":[{"given":"Mojgan","family":"Afkhami","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Neyshabur, P. O. Box 91136-899, Neyshabur, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kazem","family":"Khashyarmanesh","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,6,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.11.034"},{"key":"rf3","doi-asserted-by":"crossref","first-page":"241","DOI":"10.21136\/CMJ.1969.100891","volume":"19","author":"Cs\u00e1k\u00e1ny B.","journal-title":"Czechoslovak Math. J."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809088"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"171","DOI":"10.21136\/CMJ.1975.101307","volume":"25","author":"Zelinka B.","journal-title":"Czechoslovak Math. J."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500360","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,16]],"date-time":"2020-08-16T07:00:48Z","timestamp":1597561248000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500360"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,16]]},"references-count":5,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2014,6,16]]},"published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.1142\/S1793830914500360"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500360","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,16]]}}}