A classification of graphs whose subdivision graphs are locally $G$-distance transitive

Details A classification of graphs whose subdivision graphs are locally $G$-distance transitive A classification of graphs whose subdivision graphs are locally $G$-distance transitive

2011-03-30

arxiv.org/abs/1103.5846v1

Mathematics

Combinatorics

10 pages

Scientific paper

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.

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