Let ˙G = (G, σ) be a signed graph, and let ρ( ˙G ) (resp. λ1( ˙G )) denote the spectral radius
(resp. the index) of the adjacency matrix A( ˙G) . In this paper we detect the signed graphs
achieving the minimum spectral radius m(SRn), the maximum spectral radius M(SRn),
the minimum index m(In) and the maximum index M(In) in the set U_n of all unbalanced
connected signed graphs with n ≥ 3 vertices. From the explicit computation of the four
extremal values it turns out that the difference m(SRn)−m(In) for n ≥ 8 strictly increases
with n and tends to 1, whereas M(SRn) − M(In) strictly decreases and tends to 0