论文标题
$ k_6 \ square k_7 $的可观数量是$ 18 $
The achromatic number of $K_6\square K_7$ is $18$
论文作者
论文摘要
如果任何两种不同的颜色$ c_1，c_2 \ in c $中有一个edge $ \ {v_2 \} \ in E（g）$，则$ g $的顶点着色$ f：v（g）\ to c $的c $是完整的。 $ g $的可观数字是最大数字$ \ mathrm {achr}（g）$ $ g $的完整顶点着色。在论文中，证明$ \ mathrm {achr}（k_6 \ square k_7）= 18 $。此结果最终确定了$ \ mathrm {achr}（k_6 \ square k_q）$的确定。
A vertex colouring $f:V(G)\to C$ of a graph $G$ is complete if for any two distinct colours $c_1,c_2\in C$ there is an edge $\{v_1,v_2\}\in E(G)$ such that $f(v_i)=c_i$, $i=1,2$. The achromatic number of $G$ is the maximum number $\mathrm{achr}(G)$ of colours in a proper complete vertex colouring of $G$. In the paper it is proved that $\mathrm{achr}(K_6\square K_7)=18$. This result finalises the determination of $\mathrm{achr}(K_6\square K_q)$.
