Abstract
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.