Subgraphs.

We say that \(G' = (V', E')\) is a subgraph of \(G = (V, E)\text{,}\) and write \(G' \subseteq G\text{,}\) provided \(V' \subseteq V\) and \(E' \subseteq E\text{.}\)

We say that \(G' = (V', E')\) is an induced subgraph of \(G = (V, E)\) provided \(V' \subseteq V\) and every edge in \(E\) whose vertices are still in \(V'\) is also an edge in \(E'\text{.}\)