{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T09:50:36Z","timestamp":1767865836376,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>It is well-known that eigenvalues of graphs can be used to describe structural properties and parameters of graphs. A theorem of Nosal and Nikiforov states that if $G$ is a triangle-free graph with $m$ edges, then $\\lambda (G)\\le \\sqrt{m}$, equality holds if and only if $G$ is a complete bipartite graph. Recently, Lin, Ning and Wu [Combin. Probab. Comput. 30 (2021)] proved a generalization for non-bipartite triangle-free graphs. Moreover, Zhai and Shu [Discrete Math. 345 (2022)] presented a further improvement. In this paper, we present an alternative method for proving the improvement by Zhai and Shu. Furthermore, the method can allow us to give a refinement on the result of Zhai and Shu for non-bipartite graphs without short odd cycles.<\/jats:p>","DOI":"10.37236\/11236","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T01:21:43Z","timestamp":1666056103000},"source":"Crossref","is-referenced-by-count":10,"title":["The Maximum Spectral Radius of Non-Bipartite Graphs Forbidding Short Odd Cycles"],"prefix":"10.37236","volume":"29","author":[{"given":"Yongtao","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuejian","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,10,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i4p2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i4p2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T01:21:44Z","timestamp":1666056104000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i4p2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,7]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,10,6]]}},"URL":"https:\/\/doi.org\/10.37236\/11236","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,7]]},"article-number":"P4.2"}}