几类卡氏积图的控制数

THE DOMINATION NUMBERS FOR SOME CLASSES OF CARTESIAN PRODUCT GRAPHS

主要给出了卡氏积图Km×Kn,Sm×Sn,Sm×Cn,Sm×Pn的控制数,其中km为m阶完全图,Cn是n圈,Pn是长度为n－1的路,Sm是星图.主要结果如下;γ（Km×Kn）=min{m,n};γ（Sm×Sn）=min{m＋1,n＋1}nγy（Sm×Cn）=n（m≥4）;γ（Sm×Pn）=n（m≥4）.

The domination numbers of Cartesian product graphs Km ×Kn,Sm × Sn,Sm× Cn and Sm× Pn are given, where Km is the Complete graph of order m, Sm the star graph,Cn the n-cycle, Pn the n -path. The main results are as follows:γ(Km× Kn) = min{m,n}; γ(Sm× Sn) = min{m + 1,n + 1};γ(Sm× Cn) = n (m ≥ 4); γ(Sm× Pn) = n (m≥ 4).