Strong product of graphs

In graph theory, the strong product G ⊠ H of graphs G and H is a graph such that

The strong product is also called the normal product and AND product. It was first introduced by Sabidussi in 1960.

For example, the king's graph, a graph whose vertices are squares of a chessboard and whose edges represent possible moves of a chess king, is a strong product of two path graphs.

The Shannon capacity of a graph is defined from the independence number of its strong products with itself, by the formula

László Lovász showed that Lovász theta function is multiplicative:

He used this fact to upper bound the Shannon capacity by the Lovász number.

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