Intersection of Graphs

Topics: Graph Theory

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(definition)

Let $G_1$ and $G_2$ be graphs with vertex sets $V_1$ and $V_2$ and edge sets $E_1$ and $E_2$ respectively.

We define the intersection of both graphs, denoted $G_1\cap G_2$, as the graph that consists of the vertex set $V_1\cap V_2$ and edge set $E_1\cap E_2$.

$G_1\cap G_2$ is a subgraph of both graphs.

Compare the union of graphs.