was
dened. For a graph G of size m, the double-rotation graph R2(G) is dened as that
graph whose vertices are the
m
2
edge-induced subgraphs of size 2 in G, and where
vertices F and H are adjacent in R2(G) if and only if there exists a pairing of the two
edges of F with the two edges of H (one edge of F and one edge of H in each pair)
such that the two edges in each pair are adjacent.