Is $O(|V||E|)$ polynomial time? If an algorithm runs in $O(|V||E|)$, is its running time bounded by some polynomial of $|V|+|E|$? If not, what is its running time called?
Since $(a+b)^2 = a^2 + 2ab + b^2 \geq 2ab$, it is indeed true that $|V||E|$ is bounded by a polynomial in $|V|+|E|$.