The crossing number of K1,3,n and K2,3,n

In this article, we will determine the crossing number of the complete tripartite graphs K_1,3,n and K_2,3,n. Our proof depends on Kleitman's results for the complete bipartite graphs D. J. Kleitman, The crossing number of K_5,n. J. Combinatorial Theory 9 (1970) 315-323].