Lexicographic product of graphs
In graph theory, the lexicographic product or (graph) composition G ∙ H of graphs G and H is a graph such that * the vertex set of G ∙ H is the cartesian product V(G) × V(H); and * any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent with x in G or u = x and v is adjacent with y in H. If the edge relations of the two graphs are order relations, then the edge relation of their lexicographic product is the corresponding lexicographic order. The lexicographic product was first studied by Felix Hausdorff. As showed, the problem of recognizing whether a graph is a lexicographic product is equivalent in complexity to the graph isomorphism problem. (Wikipedia).
