  The subdivision graph $S(\Sigma)$ of a connected graph $\Sigma$ is
constructed by adding a vertex in the middle of each edge. In a previous paper
written with Cheryl E. Praeger, we characterised the graphs $\Sigma$ such that
$S(\Sigma)$ is locally $(G,s)$-distance transitive for $s\leq 2\,
diam(\Sigma)-1$ and some $G\leq Aut(\Sigma)$. In this paper, we solve the
remaining cases by classifying all the graphs $\Sigma$ such that the
subdivision graphs is locally $(G,s)$-distance transitive for $s\geq 2\,
diam(\Sigma)$ and some $G\leq Aut(\Sigma)$. In particular, their subdivision
graph are always locally $G$-distance transitive, except for the complete
graphs.

Combinatorics;Group Theory