In mathematics, a graph product is a certain kind of binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H with the following properties:
The following table shows the most common graph products, with ∼ denoting “is connected by an edge to”:
Name | Condition for (u1, u2) ∼ (v1, v2). | Dimensions | Example |
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Cartesian product | ( u1 = v1 and u2 ∼ v2 ) or ( u1 ∼ v1 and u2 = v2 ) |
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Tensor product | u1 ∼ v1 and u2 ∼ v2 | ||
Lexicographical product | u1 ∼ v1 or ( u1 = v1 and u2 ∼ v2 ) |
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Strong product (Normal product, AND product) |
( u1 = v1 and u2 ∼ v2 ) or ( u1 ∼ v1 and u2 = v2 ) or ( u1 ∼ v1 and u2 ∼ v2 ) |
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Co-normal product (disjunctive product, OR product) |
u1 ∼ v1 or u2 ∼ v2 |
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Rooted product | see article |
In general, a graph product is determined by any condition for (u1, u2) ∼ (v1, v2) that can be expressed in terms of the statements u1 ∼ v1, u2 ∼ v2, u1 = v1, and u2 = v2.