Lower bound on the number of the maximum genus embedding of $K_{n,n}$
  In this paper, we provide an method to obtain the lower bound on the number of the distinct maximum genus embedding of the complete bipartite graph Kn;n (n be an odd number), which, in some sense, improves the results of S. Stahl and H. Ren. 
Guanghua Dong, Han Ren, Ning Wang, Yuanqiu Huang
math.CO