Graphs With Smallest Forgotten Index

The forgotten topological index of a molecular graph $g$ is defined as $f(g)=sum_{vin v(g)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $g$. the first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $gamma=1,2$, the first throughthe fourth for $gamma=3$, and the first and the second for $gamma=4,5$ are determined. these results are compared with those obtained for the first zagreb index.