Locally s-distance transitive graphs and pairwise transitive designs
Combinatorics
2013-08-05 v1
Abstract
The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give a general construction for this case.
Cite
@article{arxiv.1308.0401,
title = {Locally s-distance transitive graphs and pairwise transitive designs},
author = {Alice Devillers and Michael Giudici and Cai Heng Li and Cheryl E. Praeger},
journal= {arXiv preprint arXiv:1308.0401},
year = {2013}
}
Comments
22 pages, has been accepted for publication in J. Comb. Theory Series A