Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is graph-isomorphism complete and that the stable partitions of binding graphs by the Weisfeiler-Lehman (WL) algorithm produce automorphism partitions. To test the isomorphism of two graphs $G$ and $H$, one computes the stable graph of the binding graph $[G\uplus H]$ for the disjoint union graph $G\uplus H$. The automorphism partition reveals the isomorphism of $G$ and $H$. Because the WL algorithm is a polynomial-time procedure, the claim can be made that the graph-isomorphism problem is in complexity class $\mathtt{P}$.

翻译：给定一个图$G$，通过在$G$的每对顶点之间添加一个唯一的新顶点与之相邻，得到的图$[G]$称为$G$的绑定图。本文证明绑定图类构成图同构完全类，且Weisfeiler-Lehman（WL）算法对绑定图计算得到的稳定划分可产生自同构划分。要判定两个图$G$和$H$是否同构，只需对不交并图$G\uplus H$的绑定图$[G\uplus H]$计算稳定图。自同构划分即可揭示$G$和$H$的同构性。由于WL算法是多项式时间过程，因此可断言图同构问题属于复杂度类$\mathtt{P}$。