{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T05:57:13Z","timestamp":1767851833052,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a graph of order $n$ with signless Laplacian eigenvalues $q_1, \\ldots,q_n$ and Laplacian eigenvalues $\\mu_1,\\ldots,\\mu_n$.  It is proved that for any real number $\\alpha$ with $0 &lt; \\alpha\\leq1$ or $2\\leq\\alpha &lt;  3$, the inequality $q_1^\\alpha+\\cdots+ q_n^\\alpha\\geq \\mu_1^\\alpha+\\cdots+\\mu_n^\\alpha$ holds, and for any real number $\\beta$ with $1 &lt; \\beta &lt; 2$, the inequality $q_1^\\beta+\\cdots+ q_n^\\beta\\le \\mu_1^\\beta+\\cdots+\\mu_n^\\beta$ holds.  In both inequalities, the equality is attained (for $\\alpha \\notin \\{1,2\\}$) if and only if $G$ is bipartite.<\/jats:p>","DOI":"10.37236\/387","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:10:37Z","timestamp":1578715837000},"source":"Crossref","is-referenced-by-count":22,"title":["On Sum of Powers of the  Laplacian and Signless Laplacian Eigenvalues of Graphs"],"prefix":"10.37236","volume":"17","author":[{"given":"Saieed","family":"Akbari","sequence":"first","affiliation":[]},{"given":"Ebrahim","family":"Ghorbani","sequence":"additional","affiliation":[]},{"given":"Jacobus H.","family":"Koolen","sequence":"additional","affiliation":[]},{"given":"Mohammad Reza","family":"Oboudi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,8,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r115\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:27:50Z","timestamp":1579303670000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/387","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,16]]},"article-number":"R115"}}