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arXiv · 1308.0401

Locally s-distance transitive graphs and pairwise transitive designs

Alice Devillers·Michael Giudici·Cai Heng Li·Cheryl E. Praeger
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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.

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Alice Devillers, Michael Giudici, Cai Heng Li, Cheryl E. Praeger. 2013-08-02. Locally s-distance transitive graphs and pairwise transitive designs. https://arxiv.org/abs/1308.0401

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