To determine which compound is not aromatic, we need to apply the criteria for aromaticity.$\\$A compound is aromatic if it satisfies the following conditions:$\\$• It is cyclic and planar.$\\$• It has a conjugated system of $\pi$ electrons.$\\$• It follows Hückel's rule: $4n+2$ $\pi$ electrons, where $n$ is a non-negative integer.$\\$Let's analyze each option:$\\$Option 1:$\\$• The compound is cyclopropenyl cation.$\\$• It is cyclic and planar with 2 $\pi$ electrons.$\\$• It satisfies Hückel's rule ($4n+2 = 2$ for $n = 0). \\$• Therefore, it is aromatic.$\\$Option 2:$\\$• The compound is tropylium cation.$\\$• It is cyclic and planar with 6 $\pi$ electrons.$\\$• It satisfies Hückel's rule ($4n+2 = 6$ for $n = 1). \\$• Therefore, it is aromatic.$\\$Option 3:$\\$• The compound is cyclopropenyl anion.$\\$• It is cyclic and planar with 4 $\pi$ electrons.$\\$• It does not satisfy Hückel's rule ($4n+2 \neq 4$ for any $n). \\$• Therefore, it is not aromatic.$\\$Option 4:$\\$• The compound is cyclooctatetraene.$\\$• It is not planar in its most stable conformation.$\\$• It has 8 $\pi$ electrons, which does not satisfy Hückel's rule.$\\$• Therefore, it is not aromatic.$\\$Conclusion:$\\$Option 4, cyclooctatetraene, is not an aromatic compound.$\\$This corresponds to the correct answer.