{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:17Z","timestamp":1753893857376,"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 simple graph with no even cycle, called an odd-cycle\u00a0graph. Cavers et al. [Linear Algebra Appl. 436(12):4512-1829, 2012] showed that the\u00a0spectral radius of $G^\\sigma$ is the same for every orientation\u00a0$\\sigma$ of $G$, and equals the maximum matching root of $G$. They\u00a0proposed a conjecture that the graphs which attain the maximum skew\u00a0spectral radius among the odd-cycle graphs $G$ of order $n$ are\u00a0isomorphic to the odd-cycle graph with one vertex degree $n-1$ and\u00a0size $m=\\lfloor 3(n-1)\/2\\rfloor$. By using the Kelmans\u00a0transformation, we give a proof to the conjecture. Moreover, sharp\u00a0upper bounds of the maximum matching roots of the odd-cycle graphs\u00a0with given order $n$ and size $m$ are given and extremal graphs are\u00a0characterized.<\/jats:p>","DOI":"10.37236\/4919","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:25:18Z","timestamp":1578702318000},"source":"Crossref","is-referenced-by-count":2,"title":["Solution to a Conjecture on the Maximum Skew-Spectral Radius of Odd-Cycle Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Xiaolin","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueliang","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huishu","family":"Lian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,3,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p71\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p71\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:23:23Z","timestamp":1579256603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p71"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4919","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,3,23]]},"article-number":"P1.71"}}