Deleting Vertices and Interlacing of $A_\alpha$ Eigenvalues of a Graph

Abstract:

      Let $G$ be simple graph with vertex set $V$ and edge set $E$. In this paper, we establish an interlacing inequality between the $A_{\alpha}$ eigenvalues of $G$ and its subgraph $G-U$, where $U\subseteq V$. Moreover, as an application, this interlacing property can be used to deduce some $A_{\alpha}$ spectral conditions concerning the independence number, cover number, Hamiltonian property and spanning tree of a graph, respectively.