Iwip endomorphisms of free groups and fixed points of graph selfmaps

In a paper from 2011, Jiang, Wang and Zhang studied the fixed points and fixed subgroups of selfmaps on a connected finite graph or a connected compact hyperbolic surface $X$. In particular, for any selfmap $f:X\to X$, they proved that a certain quantity defined in terms of the characteristic $\text{chr}(f,\text{F})$ and the index $\text{ind}(f,\text{F})$ of a fixed point class $\text{F}$ of $f$ is bounded below by $2\chi (X)$, where $\chi (X)$ is the Euler characteristic of $X$. In this paper, we give a sufficient condition for when equality holds and hence we partially answer a question of Jiang, by studying iwip outer endomorphisms of free groups acting on stable trees.