论文标题
关于两个完整图的笛卡尔产品的可观数量
On the achromatic number of the Cartesian product of two complete graphs
论文作者
论文摘要
一个顶点着色$ f：v（g）\ to a Graph $ g $的c $如果对于任何$ c_1，c_2 \ in c $ in c $ c_1 \ ne c_1 \ ne c_2 $ in $ g $ a相afacecent $ v_1，v_2，v_2 $，v_2 $，$ f（v_1 $ f（v_1 $ f（v_1 $ f（v_1）= c_1 $ f（v_1 $ f（v_1 $ f（v_1 $ f（c_1 $ f（c_1）， $ g $的可观数字是最大数字$ \ mathrm {achr}（g）$ $ g $的完整顶点着色。令$ G_1 \ Square G_2 $表示图形的笛卡尔产品$ g_1 $和$ g_2 $。在论文中，$ \ mathrm {achr}（k_ {r^2+r+1} \ square k_q）$是针对无限数量的$ q $ s确定的，前提是$ r $是有限的投影平面订单。
A vertex colouring $f:V(G)\to C$ of a graph $G$ is complete if for any $c_1,c_2\in C$ with $c_1\ne c_2$ there are in $G$ adjacent vertices $v_1,v_2$ such that $f(v_1)=c_1$ and $f(v_2)=c_2$. The achromatic number of $G$ is the maximum number $\mathrm{achr}(G)$ of colours in a proper complete vertex colouring of $G$. Let $G_1\square G_2$ denote the Cartesian product of graphs $G_1$ and $G_2$. In the paper $\mathrm{achr}(K_{r^2+r+1}\square K_q)$ is determined for an infinite number of $q$s provided that $r$ is a finite projective plane order.
