圈和路的笛卡尔积的H-强迫数

The H-Force Number of the Cartesian Product of a Cycle with a Path

通过研究笛卡尔积的定义得到了圈和路作笛卡尔积后得到的图形,探讨了所得图形的H-强迫集与H-强迫数问题.利用寻找非哈密尔顿圈的方法证明了主要结论:设Ck表示k个顶点的圈,Pl表示l个顶点的路,G=Ck×Pl表示Ck与Pl的笛卡尔积.则当k为偶数时,图G的H-强迫数为kl2;当k为奇数时,图G的H-强迫数为kl.

The Cartesian product of a cycle with a path was obtained by the definition of Cartesian product. An exploration was made on the H-force set and H-force number of these graphs. By using the method of searching non-hamiltonian cycle, the conclusion is proved： Let Ca be a cycle of order k, P1 be a path of order kl l. G = Ck × Pt is the Cartesian product of Ca and Pt. Then the H-force number of G is k- when k is even and the H-force number of G is kl when k is odd