六阶图C_6+3K_2与P_n,C_n的联图交叉数

The crossing number of the join product of C_6+3K_2 with P_n and C_n

用P_n表示n个点的路,C_n表示长为n的圈,C_6+3K_2表示圈C_6添加三条相邻的边3K_2=C_3得到的图.在Kleitman给出的完全二部图的交叉数cr(K_(6,n))=Z(6,n)的基础上,得到了特殊六阶图C_6+3K_2与路P_n,圈C_n的联图交叉数分别为Z(6,n)+3[n/2]+2与Z(6,n)+3[n/2]+4.

Let Pn be the path on n vertices, Cn be the cycle with n edges, C6 ＋ 3K2 be the graph which is obtained from the cycle C6 by adding three adjacent edges. In the paper, for special graph C6 ＋ 3K2, we give the crossing numbers of its join product with the path Pn as well as the cycle Cn are Z（6, n） ＋3[n/2] ＋2 and Z（6,n） ＋3[n/2] ＋4. Our proof depends on Kleitman＇s results for the complete bipartite graph cr（K6, n） = Z（6, n）.