Locally triangular graphs and rectagraphs with symmetry

@article{Bamberg2015LocallyTG,
title={Locally triangular graphs and rectagraphs with symmetry},
author={John Bamberg and Alice Devillers and Joanna B. Fawcett and C. Praeger},
journal={J. Comb. Theory, Ser. A},
year={2015},
volume={133},
pages={1-28}
}

Abstract Locally triangular graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-arc lies in a unique quadrangle. A graph Γ is locally rank 3 if there exists G ⩽ Aut ( Γ ) such that for each vertex u , the permutation group induced by the vertex stabiliser G u on the neighbourhood Γ ( u ) is transitive of rank 3. One natural place to seek locally rank 3 graphs is among the locally triangular graphs, where every induced… Expand