论文标题
最大的$a_α$ - 图形值的总和
On the sum of the largest $A_α$-eigenvalues of graphs
论文作者
论文摘要
For every real $0\leq α\leq 1$, Nikiforov defined the $A_α$-matrix of a graph $G$ as $A_α(G)=αD(G)+(1-α)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the degree diagonal matrix of a graph $G$, respectively. $a_α（g）$的特征值称为$ g $的$a_α$ eigenValues。令$ s_k（a_α（g））$为$ k $a_α$ -eigenValues $ g $的总和。在本文中，我们在$ s_k（a_α（g））$上介绍了几个上限和下限，并在某些情况下表征了极端图，可以将其视为$ k $最大的邻接矩阵特征值和无标志性laplacian laplacian矩阵的共同概括。此外，还提供了$ S_K（A_α（G））$的某些图形操作。
For every real $0\leq α\leq 1$, Nikiforov defined the $A_α$-matrix of a graph $G$ as $A_α(G)=αD(G)+(1-α)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the degree diagonal matrix of a graph $G$, respectively. The eigenvalues of $A_α(G)$ are called the $A_α$-eigenvalues of $G$. Let $S_k(A_α(G))$ be the sum of $k$ largest $A_α$-eigenvalues of $G$. In this paper, we present several upper and lower bounds on $S_k(A_α(G))$ and characterize the extremal graphs for certain cases, which can be regard as a common generalization of the sum of $k$ largest eigenvalues of adjacency matrix and signless Laplacian matrix of graphs. In addition, some graph operations on $S_k(A_α(G))$ are presented.
