关于叉积图控制数的一点注记

A Note on the Domination Numbers forCross Products of Graphs

设γ（Ｇ）表示图Ｇ的控制数，ＧＨ表示两个图Ｇ和Ｈ的叉积．ＳＧｒａｖｉｅｒ［１］提出了如下猜想：对任意图Ｇ和Ｈ，均有γ（ＧＨ）≥γ（Ｇ）γ（Ｈ）．本文给出了该猜想的反例，从而说明了该猜想是不正确的．

Let γ(G) denote the domination number of graph G, GH be the cross products of graphs G and H . S Gravier posed a conjecture as follows: For all graphs G and H, γ(GH)≥γ(G)γ(H) . In this note, we give a counterexample to the conjecture, which proves this conjecture is not true.