一种改进图同构算法的多项式图扩展过程
A polynomial graph extension procedure for improving graph isomorphism algorithms
摘要：
我们在这个简短的说明中提出了一个多项式图扩展过程，可以用来改善任何图同构算法。该构造从输入图的同构约束（由$G(V,E)$和$G'(V',E')$表示）传播新的约束。因此，来自$G$和$G'$的边结构的信息被“散列”到扩展图的加权边中。一个双射映射是初始图的同构当且仅当它是扩张图的同构。这样，该构造使得能够识别不能由任何同构$h^*:V \to V'$映射的顶点对$i\in V$和$i'\in V'$（例如，如果$i$和$i'$的扩展边不同）。构造了一个禁止矩阵$F$，它对所有不相容映射对$(i,i')$进行编码，以便由不同的算法使用。此外，对许多图类的测试表明，矩阵$F$可能只为每个$i \in V$留下一个兼容元素。
英文摘要：
We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by $G(V,E)$ and $G'(V',E')$). Thus, information from the edge structures of $G$ and $G'$ is "hashed" into the weighted edges of the extended graphs. A bijective mapping is an isomorphism of the initial graphs if and only if it is an isomorphism of the extended graphs. As such, the construction enables the identification of pair of vertices $i\in V$ and $i'\in V'$ that can not be mapped by any isomorphism $h^*:V \to V'$ (e.g. if the extended edges of $i$ and $i'$ are different). A forbidding matrix $F$, that encodes all pairs of incompatible mappings $(i,i')$, is constructed in order to be used by a different algorithm. Moreover, tests on numerous graph classes show that the matrix $F$ might leave only one compatible element for each $i \in V$.
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