Subdivided double

Summary

In graph theory, the subdivided double is a construction used to transform a 4-regular graph into a larger 4-regular graph. It consists of two steps: subdividing every edge into a path of two edges (with a new vertex in the middle of each path), and then replacing every vertex of the original graph with two copies, both adjacent to the same subdivision vertices. Potočnik, Verret, and Wilson use the notation $\operatorname{SDD}(G)$ to denote the subdivided double of a graph $G$. It was named as the subdivided double earlier, by Potočnik and Wilson.