1.1 Constructing Graphs from Other Graphs

Definition. Disjoint

• $G_{1}$,
  • graph
• $G_{2}$,
  • graph

$G_{1}$ and $G_{2}$ is said to be disjoint if

• $V(G_{1}) \cap V(G_{2}) \eq \emptyset$,
• $E(G_{1}) \cap E(G_{2}) \eq \emptyset$

■

Definition. Union

• $G_{1}$,
  • graph
• $G_{2}$,
  • graph

The union of $G_{1}$ and $G_{2}$ is a graph $G$ whose vertex set and edge set are $V(G_{1}) \cup V(G_{2})$ and $E(G_{1}) \cup E(G_{2})$ respectively. We write $G_{1} \cup G_{2}$.

■

Definition. Components

■