Subgraph

Definition

Let $G = (V, E)$ be a graph. A subgraph of $G$ is a graph $H = (V', E')$ with $V' \subseteq V$ and $E' \subseteq E$. Each edge of $E'$ has both ends in $V'$, because $H$ is a graph.

Remarks

A subgraph is spanning if $V' = V$. An induced subgraph keeps all edges of $G$ between the chosen vertices. In the cycle $C_4$ with vertices $1, 2, 3, 4$, the path $1 - 2 - 3$ is a subgraph.

Explanations

L1 human

To get a subgraph, delete some vertices and some edges of a graph. When you delete a vertex, you must also delete the edges at that vertex.