Proper Distance in Edge-Colored Hypercubes
Applied Mathematics and Computation
An edge-colored path is called properly colored if no two consecutive edges have the same color. An edge-colored graph is called properly connected if, between every pair of vertices, there is a properly colored path. Moreover, the proper distance between vertices u and v is the length of the shortest properly colored path from u to v. Given a particular class of properly connected colorings of the hypercube, we consider the proper distance between pairs of vertices in the hypercube.
Cheng, Eddie, Colton Magnant, Dhruv Medarametla.
"Proper Distance in Edge-Colored Hypercubes."
Applied Mathematics and Computation, 313: 384-391.