Optimal geodesic cycles embedding of Möbius cubes
نویسندگان
چکیده
For two vertices X,Y ∈ 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 ≤ l ≤ |V (G)|. In this paper, we show that the n-dimensional Möbius cube MQn is geodesic 2-pancyclic for n ≥ 3. This result is optimal in the sense that there is no geodesic 1-cycle with two adjacent vertices in MQn.
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