  Let $G_w$ be a weighted graph. The number of the positive, negative and zero
eigenvalues in the spectrum of $G_w$ are called positive inertia index,
negative inertia index and nullity of $G_w$, and denoted by $i_{+}(G_w)$,
$i_{-}(G_w)$, $i_{0}(G_w)$, respectively. In this paper, sharp lower bound on
the positive (resp. negative) inertia index of weighted bicyclic graphs of
order $n$ with pendant vertices is obtained. Moreover, all the weighted
bicyclic graphs of order $n$ with at most two positive, two negative and at
least $n-4$ zero eigenvalues are identified, respectively.

Combinatorics