{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:20Z","timestamp":1787337020390,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>Given a matrix M of size n, the digraph D on n vertices is said to be the digraph ofM , when $M_{ij}\\neq 0$ if and only if (v,sub&gt;i,v,sub&gt;j) is an arc of D. We give a necessary condition, called strong quadrangularity, for a digraph to be the digraph of a unitary matrix. With the use of such a condition, we show that a line digraph $\\overrightarrow{L}D$ is the pattern of a unitary matrix if and only if D is Eulerian. It follows that, if D is strongly connected and $\\overrightarrow{L}D$ is the digraph of a unitary matrix, then $\\overrightarrow{L}D$ is Hamiltonian. We observe that strong quadrangularity is sufficient to show that disconnected strongly regular graphs are the digraphs of unitary matrices and that n-paths, n-paths with loops at each vertex, n-cycles, directed trees, and trees are not.<\/jats:p>","DOI":"10.1137\/s0895479802410293","type":"journal-article","created":{"date-parts":[[2003,7,12]],"date-time":"2003-07-12T09:30:34Z","timestamp":1058002234000},"page":"295-300","source":"Crossref","is-referenced-by-count":37,"title":["On the Digraph of a Unitary Matrix"],"prefix":"10.1137","volume":"25","author":[{"given":"Simone","family":"Severini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous,\n                      One\u2010dimensional quantum walks\n                      , in Proceedings of the 33rd ACM Symposium on Theory of Computing, ACM, New York, 2001, pp. 50\u201359.","DOI":"10.1145\/380752.380757"},{"key":"R2","unstructured":"A. Ambainis, J. Kempe, and U. Vazirani,\n                      Quantum walks on graphs\n                      , in Proceedings of the 33rd ACM Symposium on Theory of Computing, ACM, New York, 2001, pp. 60\u201369."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325708"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623714"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)10051-4"},{"key":"R6","first-page":"197","volume":"2","author":"Gr\u00f6ssing Gerhard","year":"1988","journal-title":"Complex Systems"},{"key":"R7","volume-title":"Quantum probability","author":"Gudder Stanley","year":"1988"},{"key":"R8","unstructured":"L. Lov\u00e1sz, Random walks on graphs: a survey, Bolyai Soc. Math. Stud., Vol. 2, J\u00e1nos Bolyai Math. Soc., Budapest, 1996, 353\u201339797a:60097"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02199356"},{"key":"R10","first-page":"193","volume":"116","author":"Prisner Erich","year":"1996","journal-title":"Congr. Numer."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626265"},{"key":"R12","volume-title":"Graph theory","author":"Tutte W.","year":"1984"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479802410293","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:41:11Z","timestamp":1787334071000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479802410293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479802410293"],"URL":"https:\/\/doi.org\/10.1137\/s0895479802410293","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}