 Variations on this concept involving vertex colorings or more general walks on a graph have been studied by several authors including Barát and Varjú, Barát and Wood (2005), Brešar and Klavžar (2004), and Kündgen and Pelsmajer.Consider a pentagon, that is, a cycle of five vertices.If we color the edges with two colors, some two adjacent edges will have the same color x; the path formed by those two edges will have the repetitive color sequence xx.