{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T23:05:01Z","timestamp":1773183901087,"version":"3.50.1"},"reference-count":14,"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":[[2013,9]]},"abstract":"<jats:p> The independence number of a graph is defined as the maximum size of a set of pairwise non-adjacent vertices and the spectral radius is defined as the maximum eigenvalue of the adjacency matrix of the graph. Xu et al. in [The minimum spectral radius of graphs with a given independence number, Linear Algebra and its Applications431 (2009) 937\u2013945] determined the connected graphs of order n with independence number [Formula: see text] which minimize the spectral radius. In this paper, we show that the graph obtained from a path of order \u03b1 by blowing up each vertex to a clique of order k minimizes the spectral radius among all connected graphs of order k\u03b1 with independence number \u03b1 for \u03b1 = 3, 4 and conjecture that this is true for all \u03b1 \u2208 \u2115. <\/jats:p>","DOI":"10.1142\/s1793830913500171","type":"journal-article","created":{"date-parts":[[2013,7,11]],"date-time":"2013-07-11T01:34:11Z","timestamp":1373506451000},"page":"1350017","source":"Crossref","is-referenced-by-count":13,"title":["GRAPHS WITH SMALL INDEPENDENCE NUMBER MINIMIZING THE SPECTRAL RADIUS"],"prefix":"10.1142","volume":"05","author":[{"given":"XUE","family":"DU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China"}]},{"given":"LINGSHENG","family":"SHI","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2013,10,23]]},"reference":[{"key":"rf1","volume-title":"Graduate Texts in Mathematics","volume":"244","author":"Bondy J. A.","year":"2008"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02941924"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/03081080600790040"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2000.1997"},{"key":"rf6","author":"Huang S.","year":"2013","journal-title":"Graphs and Combinatorics"},{"key":"rf7","first-page":"167","volume":"2","author":"Li Q.","year":"1979","journal-title":"Acta Math. Appl. Sinica"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.12.003"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.07.010"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066438"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1253"},{"key":"rf12","first-page":"436","volume":"48","author":"Tur\u00e1n P.","year":"1941","journal-title":"Mat. Fiz. Lapok"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90069-9"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.08.025"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.03.055"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830913500171","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:22:09Z","timestamp":1565112129000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830913500171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":14,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2013,10,23]]},"published-print":{"date-parts":[[2013,9]]}},"alternative-id":["10.1142\/S1793830913500171"],"URL":"https:\/\/doi.org\/10.1142\/s1793830913500171","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}