论文标题
分离集团的光谱极端图
Spectral extremal graphs for disjoint cliques
论文作者
论文摘要
$ kk_ {r+1} $是$ k $ diseboint of $（r+1）$ - clique的联合。月亮[加拿大。 J. Math。 20（1968）95--102]和Simonovits [图理论（Proc。Colloq。，Tihany，1996）]独立地表明，如果$ n $足够大，则$ k_ {k-1} \ vee t_ {n-k+1，r} $是$ kk_的唯一极端图，是$ kk_ ^ r+1} $。在本文中，我们认为该图在所有图表中都具有最大光谱半径，而没有$ k $ discoint cliques。我们证明，如果$ g $达到所有$ n $ n $ vertex $ kk_ {r+1} $的最大光谱半径 - 免费的图形，则为足够大的$ n $，那么$ g $是同构为$ k_ {k_ {k-1} \ vee \ vee t_ {n-k+1，r} $。
The $kK_{r+1}$ is the union of $k$ disjoint copies of $(r+1)$-clique. 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 $K_{k-1}\vee T_{n-k+1,r}$ 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 prove 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 $K_{k-1}\vee T_{n-k+1,r}$.
