A sufficient Q-spectral condition for a graph to be β-deficient involving minimum degree

Abstract The deficiency of a graph G , denoted by def ( G ) , is the number of vertices unmatched under a maximum matching in G . We call G β -deficient if def ( G ) ≤ β . In this paper, by making use of the Q -spectral radius of a graph G , we present a sufficient condition for G with fixed minimum degree to be β -deficient, when G has large order.