Definition:Subgraph

Definition
A graph $$H = \left({V \left({H}\right), E \left({H}\right)}\right)$$ is called a subgraph of a graph $$G = \left({V \left({G}\right), E \left({G}\right)}\right)$$ if $$V \left({H}\right)\subseteq V \left({G}\right)$$ and $$E \left({H}\right)\subseteq E \left({G}\right)$$.

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 $$G$$

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