{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T21:28:44Z","timestamp":1770758924420,"version":"3.50.0"},"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 $kK_{r+1}$ be the graph consisting of $k$ vertex-disjoint copies of the complete graph $K_{r+1}$. Moon [Canad. J. Math. 20 (1968) 95--102] and Simonovits [Theory of Graphs (Proc. colloq., Tihany, 1996)] independently showed that if $n$ is sufficiently large, then the join of a complete graph $K_{k-1}$ and an $r$-partite Tur\u00e1n graph $T_{n-k+1,r}$ is the unique extremal graph for $kK_{r+1}$. In this paper we consider the graph which has the maximum spectral radius among all graphs without $k$ disjoint cliques. We show that if $G$ attains the maximum spectral radius over all $n$-vertex $kK_{r+1}$-free graphs for sufficiently large $n$, then $G$ is isomorphic to the join of a complete graph $K_{k-1}$ and an $r$-partite Tur\u00e1n graph $T_{n-k+1,r}$.<\/jats:p>","DOI":"10.37236\/11516","type":"journal-article","created":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T11:45:51Z","timestamp":1674819951000},"source":"Crossref","is-referenced-by-count":8,"title":["Spectral Extremal Graphs for Disjoint Cliques"],"prefix":"10.37236","volume":"30","author":[{"given":"Zhenyu","family":"Ni","sequence":"first","affiliation":[]},{"given":"Jing","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Liying","family":"Kang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,1,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T11:45:51Z","timestamp":1674819951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i1p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/11516","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,27]]},"article-number":"P1.20"}}