  Inspired by the work in \cite{sauer} regarding the classification of all the
zero-divisor graphs with six vertices, we obtain all the zero-divisor graphs
with seven vertices. Hence we classify all the zero-divisor commutative
semigroups with 8 elements. We also obtain all the connected graphs with seven
vertices which satisfies the necessary condition $\star$ of zero-divisor graphs
given in \cite{fl} but are not the zero-divisor graphs.
