  The forgotten topological index of a graph $G$, denoted by $F(G)$, is defined
as the sum of weights $d(u)^{2}+d(v)^{2}$ over all edges $uv$ of $G$ , where
$d(u)$ denotes the degree of a vertex $u$. In this paper, we give sharp upper
bounds of the F-index (forgotten topological index) over bicyclic graphs, in
terms of the order and maximum degree.
