An identification of two vertices $u$ and $v$ in a graph replaces them with a new vertex whose neighborhood is the union of the neighborhoods of $u$ and $v$. We study the {\sc ${\cal H}$-Identification} problem, which is to decide whether a given graph $G$ can be transformed (``identified'') to a graph in ${\cal H}$ by applying at most $k$ vertex identifications. We determine the classical and parameterized complexity of this problem for various subclasses ${\cal H}$ of chordal graphs, obtaining an almost complete picture for two parameters: $k$ and $n-k$. We also consider the {\sc Identification} problem, which is to test for two given graphs $G$ and $H$ if $G$ can be identified to $H$. We determine the parameterized complexity of this problem when $H$ is a graph from one of our testbed classes, taking the number of simplicial vertices of $H$ as the parameter.

翻译：在图$G$中识别两个顶点$u$和$v$，会用一个新顶点替换它们，该新顶点的邻域是$u$和$v$的邻域的并集。我们研究{\sc ${\cal H}$-识别}问题，即判断给定图$G$是否可以通过最多$k$次顶点识别操作（"识别"）转化为${\cal H}$中的图。我们针对弦图的多个子类${\cal H}$确定了该问题的经典复杂性和参数化复杂性，在$k$和$n-k$两个参数上获得了近乎完整的结论。我们还考虑了{\sc 识别}问题，即测试两个给定图$G$和$H$是否可以通过识别操作将$G$转化为$H$。我们确定了当$H$属于我们测试类中的某个图时该问题的参数化复杂性，以$H$的单形顶点数量作为参数。