In graph theory, a graph product is a binary operation on graphss. Specifically, it is an operation that takes two graphs and and produces a graph with the following properties:

• The vertex set of is the Cartesian product , where and are the vertex sets of and , respectively.

• Two vertices and of are connected by an edge, iff a condition about in and in is fulfilled.

The graph products differ in what exactly this condition is. It is always about whether or not the vertices in are equal or connected by an edge.

The terminology and notation for specific graph products in the literature varies quite a lot; even if the following may be considered somewhat standard, readers are advised to check what definition a particular author uses for a graph product, especially in older texts.

Even for more standard definitions, it is not always consistent in the literature how to handle self-loops would suggest.

Overview table

does means they must be distinct and non-adjacent. The operator symbols listed here are by no means standard, especially in older papers..

Mnemonic

is the complete graph on four vertices.

.

See also

• Graph operations

Notes

References