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arXiv · 1808.05319

Edge-transitive graphs of small order and the answer to a 1967 question by Folkman

Marston Conder·Gabriel Verret
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Abstract

In this paper, we introduce a method for finding all edge-transitive graphs of small order, using faithful representations of transitive permutation groups of small degree, and we explain how we used this method to find all edge-transitive graphs of order up to $47$, and all bipartite edge-transitive graphs of order up to $63$. We also give an answer to a 1967 question of Folkman about semi-symmetric graphs of large valency; in fact we show that for semi-symmetric graphs of order $2n$ and valency $d$, the ratio $d/n$ can be arbitrarily close to $1$.

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Marston Conder, Gabriel Verret. 2018-08-16. Edge-transitive graphs of small order and the answer to a 1967 question by Folkman. https://arxiv.org/abs/1808.05319

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