论文标题
没有未成年人和星森林的$α$索引的频谱极端结果
Spectral extremal results on the $α$-index of graphs without minors and star forests
论文作者
论文摘要
令$ g $为订单$ n $的图表，让$ a（g）$和$ d（g）$为邻接矩阵和$ g $的学位矩阵。定义凸线性组合 $a_α（g）$ a $ a（g）$和$ d（g）$ by $$a_α（g）=αd（g）+（1-α）a（g）a（g）$$对于任何实际数字$ 0 \leqα\ leq1 $。 $ g $的\ emph {$α$ -Index}是$a_α（g）$的最大特征值。在本文中，我们确定了最大$α$ index，并表征$ k_r $ sille-free图的所有极端图，$ k_ {s，t} $ sill-free Graphs和unifiend eigenvector方法的任何$ 0 <α<1 $ $ 0 <α<1 $的无星孔图。
Let $G$ be a graph of order $n$, and let $A(G)$ and $D(G)$ be the adjacency matrix and the degree matrix of $G$ respectively. Define the convex linear combinations $A_α(G)$ of $A (G)$ and $D (G) $ by $$A_α(G)=αD(G)+(1-α)A(G)$$ for any real number $0\leqα\leq1$. The \emph{$α$-index} of $G$ is the largest eigenvalue of $A_α(G)$. In this paper, we determine the maximum $α$-index and characterize all extremal graphs for $K_r$ minor-free graphs, $K_{s,t}$ minor-free graphs, and star-forest-free graphs for any $0<α<1$ by unified eigenvector approach, respectively.
