# directProduct -- Computes the direct product of two graphs

## Synopsis

• Usage:
F = directProduct(G,H)
• Inputs:
• G, an instance of the type Graph,
• H, an instance of the type Graph,
• Outputs:
• F, an instance of the type Graph, The Direct Product of G and H

## Description

This method will take in any two graphs and output the direct product of these two graphs. The vertex set of the direct product of G and H is the cartesian product of G and H's vertex sets. The keys for each vertex will be output as a sequence to represent this. Any two vertices (u,u') and (v,v') form an edge in the direct product of G and G if and only if u' is adjacent with v' and u is adjacent with v in the original graphs.

 i1 : G = graph({1,2},{{1,2}}); i2 : H = graph({3,4,5},{{3,4},{4,5}}); i3 : G'= directProduct(G,H) o3 = Graph{(1, 3) => {(2, 4)} } (1, 4) => {(2, 5), (2, 3)} (1, 5) => {(2, 4)} (2, 3) => {(1, 4)} (2, 4) => {(1, 3), (1, 5)} (2, 5) => {(1, 4)} o3 : Graph