The graph lexicographic (or lexicographical) product is the graph product denoted 
and defined by the adjacency relations (
) or (
and 
). The graph lexicographic product is also known as the
graph composition (Harary 1994, p. 21).
For a positive integer 
, the product 
with the empty graph 
is the uniform 
-fold graph blow-up of 
.
Graph lexicographic products can be computed in the Wolfram Language using GraphProduct[G1, G2, "Lexicographical"].
The "double graph" of a given graph 
is the graph lexicographic product 
.
