{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:48:34Z","timestamp":1759063714717,"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 $\\mu\\left( G\\right) $ and $\\mu_{\\min}\\left( G\\right) $ be the largest and smallest eigenvalues of the adjacency matrix of a graph $G$. Our main results are: (i) If $H$ is a proper subgraph of a connected graph $G$ of order $n$ and diameter $D$, then $$ \\mu\\left( G\\right) -\\mu\\left( H\\right) &gt;{1\\over\\mu\\left( G\\right) ^{2D}n}. $$ (ii) If $G$ is a connected nonbipartite graph of order $n$ and diameter $D$, then $$ \\mu\\left( G\\right) +\\mu_{\\min}\\left( G\\right) &gt;{2\\over\\mu\\left( G\\right) ^{2D}n}. $$ For large $\\mu $ and $D$ these bounds are close to the best possible ones.<\/jats:p>","DOI":"10.37236\/932","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:52:11Z","timestamp":1578718331000},"source":"Crossref","is-referenced-by-count":11,"title":["Revisiting Two Classical Results on Graph Spectra"],"prefix":"10.37236","volume":"14","author":[{"given":"Vladimir","family":"Nikiforov","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:04:51Z","timestamp":1579320291000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/932","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,17]]},"article-number":"R14"}}