On the minimum real roots of the adjoint polynomial of a graph

For a graph GG, we denote by h(G,x)h(G,x) the adjoint polynomial of GG. Let β(G)β(G) denote the minimum real root of h(G,x)h(G,x). In this paper, we characterize all the connected graphs GG with −(2+5)≤β(G)<−4.