{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:37:32Z","timestamp":1759639052662},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2003,12]]},"abstract":"<jats:p> Let G be a digraph, LG its line digraph and A(G) and A(LG) their adjacency matrices. We present relations between the Jordan Normal Form of these two matrices. In addition, we study the spectra of those matrices and obtain a relationship between their characteristic polynomials that allows us to relate properties of G and LG, specifically the number of cycles of a given length. <\/jats:p>","DOI":"10.1142\/s0219265903000933","type":"journal-article","created":{"date-parts":[[2004,2,11]],"date-time":"2004-02-11T05:41:30Z","timestamp":1076478090000},"page":"377-393","source":"Crossref","is-referenced-by-count":18,"title":["Algebraic properties of a digraph and its line digraph"],"prefix":"10.1142","volume":"04","author":[{"given":"C.","family":"Balbuena","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tica Aplicada III, Universitat Polit\u00e8cnica de Catalunya, Spain"}]},{"given":"D.","family":"Ferrero","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas State University, San Marcos, TX, U.S.A."}]},{"given":"X.","family":"Marcote","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tica Aplicada III, Universitat Polit\u00e8cnica de Catalunya, Spain"}]},{"given":"I.","family":"Pelayo","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tica Aplicada III, Universitat Polit\u00e8cnica de Catalunya, Spain"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01110285"},{"key":"rf2","volume-title":"Algebraic Graph theory","author":"Biggs N.","year":"1993"},{"key":"rf3","first-page":"101","volume":"20","author":"Bernau S. J.","journal-title":"Rend. Istit. Mat. Univ. Trieste"},{"key":"rf4","volume-title":"Spectra of graphs","author":"Cvetkovic M.","year":"1980"},{"key":"rf5","first-page":"871","volume":"2","author":"Flanders H.","journal-title":"Proc. Amer. Math. Soc."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1984.1676455"},{"key":"rf7","unstructured":"R. L.\u00a0Hemminger and L. W.\u00a0Beineke, Selected Topics in Graph Theory I, eds. L. W.\u00a0Beineke and R. J.\u00a0Wilson (Academic Press, London, 1978)\u00a0pp. 271\u2013305."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02854581"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.2307\/2974670"},{"key":"rf13","unstructured":"A. J.\u00a0Schwenk and R. J.\u00a0Wilson, Selected Topics in Graph Theory I, eds. L. W.\u00a0Beineke and R. J.\u00a0Wilson (Academic Press, London, 1978)\u00a0pp. 271\u2013305."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(97)00200-8"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265903000933","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:33:32Z","timestamp":1565120012000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265903000933"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12]]},"references-count":12,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2003,12]]}},"alternative-id":["10.1142\/S0219265903000933"],"URL":"https:\/\/doi.org\/10.1142\/s0219265903000933","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,12]]}}}