完全正则三部图与二部图的笛卡尔积的亏格

Genus of Cartesian Product of a Complete Regular Tripartite Graph and a Bipartite Graph

设Km,m,m(m≥1)是一个完全正则三部图,G是一个围长大于4的二部图.当G的最大度不大于2m时,本文得到完全正则三部图Km,m,m与G的笛卡尔积的亏格.我们的结果推广了Bonnington和Pisanski关于Km,m,m与偶圈的笛卡尔积的亏格.此外,我们还得到了Km,m,m与一些非二部图的笛卡尔积的不可定向亏格.

Let K_(m,m,m)(m≥1)be a complete regular tripartite graph,and G be a bipartite graph with girth greate than 4.In this paper,the genus of cartesian product of K_(m,m,m)and G with?(G)≤2m is determined.It generalize the result by Bonnington and Pisanski,which gives the genus of cartesian product of K_(m,m,m)and an even cycle Moreover,the nonorientable genera of cartesian products of K_(m,m,m)and some non-bipartite graphs are obtained.