The Aα-spectral Radius and $[a,b]$-factors in Graphs

Let $A(G)$ and $D(G)$ be the adjacency matrix and the degree matrix of G, respectively. For any real α ∈ [0,1], Nikiforov [12] defined the matrix Aα(G) as \[ Aα(G) = α D(G) + (1-α) A(G). \] An $[a,b]$-factor of a graph G is a spanning subgraph H such that a ≤ dH(v) ≤ b for any v ∈ V(G), where a and b are positive integers. In this paper, we give an upper bound of Aα-spectral radius of graphs with unique perfect matching, and then present Aα-spectral conditions for the existence of an $[a,b]$-factor in a graph. Our results extend the result of Fan et al. in [4] for the unique perfect matching and $[a,b]$-factor of graphs, and that of Zhao et al. in [16] for a $[1,b]$-odd factor of graphs.