{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:44:18Z","timestamp":1787319858028,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[1992,11]]},"abstract":"<jats:p>Let T be a tree on n vertices. The Laplacian matrix $L( T )$ is the difference of the diagonal matrix of vertex degrees and the adjacency matrix. The main result of this article is that, for \u201calmost all\u201d trees T, there is a nonisomorphic tree $T^\\prime $ such that per $L ( T ) = {\\text{per }}L ( T^\\prime )$. The proof follows the approach taken by Schwenk in [New Directions in the Theory of Graphs, F. Harary, ed., Academic Press, New York, 1973, pp. 275\u2013307]. The difficulty is finding a single pair of \u201csuper\u201d trees from which to start. The search for this pair was greatly facilitated by a new algorithm for computing Laplacian permanents of trees. This algorithm is also reported. Finally, the algorithm is used to establish inequalities for per $L ( T )$.<\/jats:p>","DOI":"10.1137\/0405036","type":"journal-article","created":{"date-parts":[[2005,2,23]],"date-time":"2005-02-23T08:04:07Z","timestamp":1109145847000},"page":"460-466","source":"Crossref","is-referenced-by-count":7,"title":["Laplacian Permanents of Trees"],"prefix":"10.1137","volume":"5","author":[{"given":"Phillip","family":"Botti","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Russel","family":"Merris","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheryl","family":"Vega","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,8]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(86)90124-2"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90127-4"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90310-X"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1080\/03081089008818029"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1021\/ma60073a001"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.21136\/CMJ.1973.101168"},{"key":"R7","unstructured":"J. von zur Gathen, Algebraic complexity theory, Technical Report, 207188, University of Toronto, Toronto, Ontario, Canada, 1988"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90091-9"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1063\/1.435862"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1080\/03081088508817680"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1964-0168585-9"},{"key":"R12","doi-asserted-by":"crossref","first-page":"397","DOI":"10.21136\/CMJ.1982.101816","volume":"32","author":"Merris Russell","year":"1982","journal-title":"Czechoslovak Math. J."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1080\/03081088908817955"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0611030"},{"key":"R15","first-page":"275","volume-title":"New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan, Ann Arbor, Mich., 1971)","author":"Schwenk Allen J.","year":"1973"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(79)90044-6"},{"key":"R17","doi-asserted-by":"crossref","first-page":"7","DOI":"10.21136\/CMJ.1986.102059","volume":"36","author":"Vrba Anton\u00edn","year":"1986","journal-title":"Czechoslovak Math. J."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1080\/03081088608817728"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0405036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:53:35Z","timestamp":1787316815000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0405036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,11]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,11]]}},"alternative-id":["10.1137\/0405036"],"URL":"https:\/\/doi.org\/10.1137\/0405036","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,11]]}}}