The Aα spectral radius of graphs with given independence number

Let [Formula: see text] be a simple graph, the independence number [Formula: see text] of [Formula: see text] is the number of vertices of the largest independent set in [Formula: see text]. Set [Formula: see text] denote the set of graphs which has order [Formula: see text] and independence number [Formula: see text], [Formula: see text] be the bipartite unicycle graphs with given independence number [Formula: see text]. In this paper, I characterized the graphs which have the minimum [Formula: see text]-spectral radius among all the connected graphs of order [Formula: see text] with independence number [Formula: see text] firstly and then got the minimum [Formula: see text]-spectral radius of graphs in [Formula: see text]. Additionally, I obtained the maximum [Formula: see text]-spectral radius of [Formula: see text].