{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T08:20:45Z","timestamp":1773130845602,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a graph of order $n$ with eigenvalues $\\lambda_1 \\geq \\cdots \\geq\\lambda_n$. Let \\[s^+(G)=\\sum_{\\lambda_i&gt;0} \\lambda_i^2, \\qquad s^-(G)=\\sum_{\\lambda_i&lt;0} \\lambda_i^2.\\] The smaller value, $s(G)=\\min\\{s^+(G), s^-(G)\\}$ is called the square energy\u00a0of $G$. In 2016, Elphick, Farber, Goldberg, and Wocjan conjectured that for every connected graph $G$ of order $n$, $s(G)\\geq n-1.$ No linear bound for $s(G)$ in terms of $n$ is known. Let $H_1, \\ldots, H_k$ be disjoint induced subgraphs of $G$. In this note, we prove that \\[s^+(G)\\geq\\sum_{i=1}^{k} s^+(H_i) \\quad \\text{ and } \\quad s^-(G)\\geq\\sum_{i=1}^{k} s^-(H_i),\\] and then use this result to prove that $s(G)\\geq \\frac{3n}{4}$ for every connected graph $G$ of order $n\\ge 4$.<\/jats:p>","DOI":"10.37236\/13467","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T14:17:45Z","timestamp":1758291465000},"source":"Crossref","is-referenced-by-count":1,"title":["A Linear Lower Bound for the Square Energy of Graphs"],"prefix":"10.37236","volume":"32","author":[{"given":"Saieed","family":"Akbari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hitesh","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bojan","family":"Mohar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shivaramakrishna","family":"Pragada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,9,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T14:17:46Z","timestamp":1758291466000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i3p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/13467","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,19]]},"article-number":"P3.53"}}