Wenger图H_m(q)是定义在有限域F_q上的q-正则二部图.根据二部图G=(X∪Y,E)的控制数为Y在X中的控制数与X在Y中的控制数之和,采用矩阵运算的方法在H_m(q)中通过构造含点数最少的控制集,说明了这两个控制数应该相等,从而确定了Wenger图的控制数.
Wenger's graph H_m(q)is a q-regular bipartite graph in the field F_q.Considering that the domination number of a bipartite graph G=(X∪Y,E)is the sum of Y's domination number in X and X's domination number in Y,by using the matrix operation,the domination set of H_m(q)with minimum cardinality was constructed.It is proved that the two domination numbers are equal,and then the domination number of H_m(q)was determined.