Embed Geodesic Cycles into Möbius Cubes

For two vertices x, y isin V (G), a cycle is called a geodesic cycle with x and y if a shortest path joining x and y lies on the cycle. A graph G is called to be geodesic k-pancyclic if any two vertices x, y on G have such geodesic cycle of length l that 2dG(x, y) + k les l les |V (G)|. In this paper, we show that the n-dimensional Moumlbius cube MQn is geodesic 2-pancyclic for n ges 3.