The crossing number of pancake graph $P_4$ is six
  The {\it crossing number} of a graph $G$ is the least number of pairwise crossings of edges among all the drawings of $G$ in the plane. The pancake graph is an important topology for interconnecting processors in parallel computers. In this paper, we prove the exact value of the crossing number of pancake graph $P_4$ is six. 
Yuansheng Yang, Bo Lv, Baigong Zheng, Xirong Xu, Ke Zhang
cs.DM math.CO