In an <acyclic directed mixed graph>, a <fixable vertex> $v$ is one whose bidirected district contains no proper directed descendant of $v$:
$$
\operatorname{dis}(v)\cap\operatorname{de}(v)=\{v\}.
$$
Here $A$ and $Y$ lie in the same district because $A\leftrightarrow Y$, and $Y$ is a directed descendant of $A$ along $A\to M\to Y$. Thus $A$ is not fixable.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 221 / 3 / ii / Solution

A vertex is fixable when its district contains no proper directed descendant of that vertex. Equivalently, $\operatorname{dis}(v)\cap\operatorname{de}(v)=\{v\}$.


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 Incoming links: Fixable vertex