The pseudo-Grundy index of a graph is the largest number of colors that can be assigned to its edges, such that for every pair of colors $i,j$, if $i < j$ then every edge colored with color $j$ is adjacent to at least one edge colored with color $i$. This index has been widely studied. A geometric graph is a graph drawn in the plane such that its vertices are points in general position, and its edges are straight-line segments. In this paper, we extend the notion of pseudo-Grundy index for geometric graphs, and present results for complete geometric graphs.

翻译：图的伪Grundy指数是指能够为其边分配的最大颜色数，使得对于任意颜色对$i,j$，若$i < j$，则每条颜色为$j$的边都至少与一条颜色为$i$的边相邻。该指数已被广泛研究。几何图是一种绘制在平面上的图，其顶点处于一般位置，边为直线段。本文扩展了几何图的伪Grundy指数概念，并给出了完全几何图的相关结果。