xyz drawing | xyz graph

An x y z embedding, also called an "x y z drawing, " is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is a vertex set of a cubic graph in which two vertices are adjacent if and only if two of their three coordinates are equal and each vertex v is connected to the three other points that lie on the three axis-parallel lines through v. A planar graph G is an x y z graph (and hence possesses an x y z embedding) if and only if G is bipartite, cubic, and 3-connected.

cubic graph | Hamming graph | straight line embedding