Subgraph

graph-theory

Definition

Subgraph

A graph $H=(V^{\prime },E^{\prime })$ is called subgraph of graph $G=(V,E)$ if it holds that:

$$V^{\prime }\subseteq V\wedge E^{\prime }\subseteq E$$

Induced Subgraph

Definition

Induced Subgraph

A subgraph $H=(V^{\prime },E^{\prime })$ of a graph $G=(V,E)$ is called an induced subgraph if it contains all edges from $E$ whose start and end nodes are included in $V^{\prime }$. That is, $E^{\prime }$ does not need to be explicitly specified but is induced by the specified but is induced by the specification of $G$ and $V^{\prime }$.

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