Let Gwβ be a weighted graph. The \textit{inertia} of Gwβ is the triple
In(Gwβ)=(i+β(Gwβ),iββ(Gwβ),i0β(Gwβ)), where
i+β(Gwβ),iββ(Gwβ),i0β(Gwβ) are the number of the positive, negative and zero
eigenvalues of the adjacency matrix A(Gwβ) of Gwβ including their
multiplicities, respectively. i+β(Gwβ), iββ(Gwβ) is called the
\textit{positive, negative index of inertia} of Gwβ, respectively. In this
paper we present a lower bound for the positive, negative index of weighted
unicyclic graphs of order n with fixed girth and characterize all weighted
unicyclic graphs attaining this lower bound. Moreover, we characterize the
weighted unicyclic graphs of order n with two positive, two negative and at
least nβ6 zero eigenvalues, respectively.Comment: 23 pages, 8figure