This work examines different notions of similarity for a pair u, v of vertices of a graph G. The considered similarity notions are either of removal type or attachment type. In the removal case, checking similarity between u and v is a matter of comparing the vertex-deleted subgraphs G−u and G−v according to a certain criterion (isomorphism, degree sequence, index, characteristic polynomial, complementarity spectrum, etc.). In the attachment case, we compare the expanded graphs $G^u\mathbf{1}$ and $G^v\mathbf{1}$ obtained by attaching a pendant vertex to u and v, respectively. The duality between vertex-removal and vertex-attachment serves as central axis for the exposition.

中文翻译：

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图的顶点移除、顶点添加和相似性的不同概念

这项工作检查了图G的一对u和v的相似性的不同概念。所考虑的相似性概念是移除类型或附件类型。在移除的情况下，检查u和v之间的相似性是根据特定标准（同构、度序列、索引、特征多项式、互补谱等）比较顶点删除子图G − u和G − v的问题。 . 在附件案例中，我们比较扩展图$G^{你}\mathbf{1个}$和$G^v\mathbf{1个}$通过分别将悬垂顶点附加到u和v获得。顶点移除和顶点附加之间的二元性作为阐述的中心轴。