{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:13:36Z","timestamp":1758824016479},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p> In spectral graph theory, the Laplacian energy of undirected graphs has been studied extensively. However, there has been little work yet for digraphs. Recently, Perera and Mizoguchi (2010) introduced the directed Laplacian matrix [Formula: see text] and directed Laplacian energy [Formula: see text] using the second spectral moment of [Formula: see text] for a digraph [Formula: see text] with [Formula: see text] vertices, where [Formula: see text] is the diagonal out-degree matrix, and [Formula: see text] with [Formula: see text] whenever there is an arc [Formula: see text] from the vertex [Formula: see text] to the vertex [Formula: see text] and 0 otherwise. They studied the directed Laplacian energies of two special families of digraphs (simple digraphs and symmetric digraphs). In this paper, we extend the study of Laplacian energy for digraphs which allow both simple and symmetric arcs. We present lower and upper bounds for the Laplacian energy for such digraphs and also characterize the extremal graphs that attain the lower and upper bounds. We also present a polynomial algorithm to find an optimal orientation of a simple undirected graph such that the resulting oriented graph has the minimum Laplacian energy among all orientations. This solves an open problem proposed by Perera and Mizoguchi at 2010. <\/jats:p>","DOI":"10.1142\/s0129054115500203","type":"journal-article","created":{"date-parts":[[2015,7,7]],"date-time":"2015-07-07T02:10:19Z","timestamp":1436235019000},"page":"367-380","source":"Crossref","is-referenced-by-count":5,"title":["Laplacian Energy of Digraphs and a Minimum Laplacian Energy Algorithm"],"prefix":"10.1142","volume":"26","author":[{"given":"Xingqin","family":"Qi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong University (Weihai), Weihai, Shandong Province, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edgar","family":"Fuller","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Virginia University, Morgantown, West Virginia, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rong","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Virginia University, Morgantown, West Virginia, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guodong","family":"Guo","sequence":"additional","affiliation":[{"name":"The Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, West Virginia, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cunquan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Virginia University, Morgantown, West Virginia, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,7,6]]},"reference":[{"key":"p_1","first-page":"1907","volume":"4","author":"Adiga C.","year":"2009","journal-title":"International Mathematical Forum"},{"key":"p_2","first-page":"80","volume":"10","author":"Adiga C.","year":"2009","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054107004644"},{"key":"p_6","first-page":"561","volume":"62","author":"Jooyandeh M. R.","year":"2009","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-006-0089-2"},{"key":"p_8","first-page":"355","volume":"59","author":"Liu J.","year":"2008","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"p_9","first-page":"35","volume":"2010","author":"Perera K.","year":"2010","journal-title":"MI Preprint Series"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.01.006"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054115500203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:26:52Z","timestamp":1565112412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054115500203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":8,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,7,6]]},"published-print":{"date-parts":[[2015,4]]}},"alternative-id":["10.1142\/S0129054115500203"],"URL":"https:\/\/doi.org\/10.1142\/s0129054115500203","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4]]}}}