{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:47:54Z","timestamp":1759063674920,"version":"3.41.2"},"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 on $n$ vertices with $r := \\lfloor n\/2 \\rfloor$ and let $\\lambda _1 \\geq\\cdots\\geq \\lambda _{n} $ be adjacency eigenvalues of $G$.  Then the H\u00fcckel energy of $G$, HE($G$), is defined as $${\\rm HE}(G) = \\cases{ \\displaystyle  \\;  2\\sum_{i=1}^{r} \\lambda_i, &amp; \\hbox{if $n= 2r$;} \\cr \\displaystyle  \\;  2\\sum_{i=1}^{\\phantom{l}r\\phantom{l}} \\lambda_i + \\lambda_{r+1}, &amp; \\hbox{if $n= 2r+1$.}\\cr } $$ The concept of H\u00fcckel energy was introduced by Coulson as it gives a good approximation for the $\\pi$-electron energy of molecular graphs. We obtain two upper bounds and a lower bound for HE$(G)$. When $n$ is even, it is shown that equality holds in both upper bounds if and only if $G$ is a strongly regular graph with parameters $(n, k, \\lambda, \\mu) = (4t^2 +4t +2,\\, 2t^2 +3t +1,\\, t^2 +2t,\\, t^2 + 2t +1),$ for positive integer $t$.  Furthermore, we will give an infinite family of these strongly regular graph whose construction was communicated by Willem Haemers to us. He attributes the construction to J.$\\,$J. Seidel.<\/jats:p>","DOI":"10.37236\/223","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:24:09Z","timestamp":1578716649000},"source":"Crossref","is-referenced-by-count":13,"title":["Bounds for the H\u00fcckel Energy of a Graph"],"prefix":"10.37236","volume":"16","author":[{"given":"Ebrahim","family":"Ghorbani","sequence":"first","affiliation":[]},{"given":"Jack H.","family":"Koolen","sequence":"additional","affiliation":[]},{"given":"Jae Young","family":"Yang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,11,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r134\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:39:55Z","timestamp":1579315195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r134"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/223","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,11,7]]},"article-number":"R134"}}