Union of graphs $G(V_1, E_1)$ and $G(V_2, E_2)$ is defined and denoted by $ G(V_1, E_1)\cup G(V_2, E_2)=G(V_1\cup V_2, E_1\cup E_2)$.
Suppose, $G_1$ with $m$ vertices and $G_2$ with $n$ vertices are two arbitrary simple graphs with $p$ and $q$ components, respectively. Also, $G_1$ and $G_2$ have $e$ edges in common. What is the maximal and the minimal number of components in $G(V_1, E_1)\cup G(V_2, E_2)$?