Definition:Subgraph

Definition

A graph $H = \struct {\map V H, \map E H}$ is called a subgraph of a graph $G = \struct {\map V G, \map E G}$ if and only if:

$\map V H \subseteq \map V G$

and:

$\map E H \subseteq \map E G$

That is to say, it contains no vertices or edges that are not in the original graph.

If $H$ is a subgraph of $G$, then:

$G$ contains $H$

$H$ is contained in $G$.

If a graph $F$ is isomorphic to a subgraph $H$ of $G$, then $F$ can be embedded in $G$.