In this paper we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical decreasing ordering and give rise to a new element of the graph: the gradation vector. We introduce the notion of minimum gradation vector as a new invariant for the graph and give polynomial algorithms to obtain it. These algorithms also output all greyscales that produce the minimum gradation vector. This way we tackle and solve a novel vectorial optimization problem in graphs that may generate more satisfactory solutions than those generated by known scalar optimization approaches.

在本文中，我们提出了图的灰度概念，即使用实区间 [0,1] 中的颜色对其顶点进行着色。任何灰度都会通过为每条边分配其顶点颜色之间的非负差异来引发另一种着色。这些边缘颜色按字典递减顺序排列，并产生图形的新元素：渐变向量。我们引入最小渐变向量的概念作为图的新不变量，并给出多项式算法来获得它。这些算法还输出产生最小灰度向量的所有灰度。通过这种方式，我们处理并解决了图形中的一个新的矢量优化问题，它可能会生成比已知标量优化方法生成的解更令人满意的解。