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arXiv · 1507.01027

Finite 2-distance transitive graphs

Brian P. Corr·Wei Jin·Csaba Schneider
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Abstract

A non-complete graph $\Gamma$ is said to be $(G,2)$-distance transitive if $G$ is a subgroup of the automorphism group of $\Gamma$ that is transitive on the vertex set of $\Gamma$, and for any vertex $u$ of $\Gamma$, the stabilizer $G_u$ is transitive on the sets of vertices at distance 1 and 2 from $u$. This paper investigates the family of $(G,2)$-distance transitive graphs that are not $(G,2)$-arc transitive. Our main result is the classification of such graphs of valency not greater than 5.

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Brian P. Corr, Wei Jin, Csaba Schneider. 2015-07-03. Finite 2-distance transitive graphs. https://arxiv.org/abs/1507.01027

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