The minimal positive index of inertia of signed unicyclic graphs.

The positive index of inertia of a signed graph Gamma, denoted by i(+)(Gamma), is the number of positive eigenvalues of the adjacency matrix A(F) including multiplicities. In this paper we investigate the minimal positive index of inertia of signed unicyclic graphs of order n with fixed girth and characterize the extremal graphs with the minimal positive index. Finally, we characterize the signed unicyclic graphs with the positive indices 1 and 2.