The digraph union of two digraphs is the digraph whose vertex set (respectively, edge set) is the union of their vertex sets (respectively, edge sets).
Given a positive integer 
, the adjacency matrix
of the digraph union of two labeled 
-digraphs is the entrywise maximum of their adjacency matrices.
If 
is a positive
integer, then the labeled 
-digraphs form a semilattice with respect to the digraph union.
