# Locally triangular graphs and rectagraphs with symmetry

@article{Bamberg2014LocallyTG,
title={Locally triangular graphs and rectagraphs with symmetry},
author={John Bamberg and Alice Devillers and Joanna B. Fawcett and Cheryl E. Praeger},
journal={J. Comb. Theory, Ser. A},
year={2014},
volume={133},
pages={1-28}
}
• Published 31 July 2014
• Mathematics
• J. Comb. Theory, Ser. A
7 Citations

## Tables from this paper

• Mathematics
J. Comb. Theory, Ser. A
• 2020
• Mathematics
• 2018
A finite graph $\G$ is said to be {\em $(G,3)$-$($connected$)$ homogeneous} if every isomorphism between any two isomorphic (connected) subgraphs of order at most $3$ extends to an automorphism \$g\in
For an integer n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}
For an integer $$n\ge 2$$n≥2, the triangular graph has vertex set the 2-subsets of $$\{1,\ldots ,n\}$${1,…,n} and edge set the pairs of 2-subsets intersecting at one point. Such graphs are known to

## References

SHOWING 1-10 OF 38 REFERENCES

• Mathematics
• 2003
We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)-arc transitive for s > 2 or G-locally primitive. Such
With any graph we can associate a group, namely its automorphism group; this acts naturally as a permutation group on the vertices of the graph. The converse idea, that of reconstructing a graph (or
• Mathematics
Eur. J. Comb.
• 1993
This paper gives a classification of all primitive affine 2-arc transitive graphs, and all finite 'bi-primitive' affine 1-arctransitive graphs such that the stabilizer of the bipartition of the vertices is primitive on each part of the antipartition.
• Mathematics
• 2003
Let Γ be a graph with diameter d ≥ 2. Recall Γ is 1-homogeneous (in the sense of Nomura) whenever for every edge xy of Γ the distance partition{{z ∈ V(Γ) | ∂(z, y) = i, ∂(x, z) = j} | 0 ≤ i, j ≤ d}is
A more general theorem is proved, showing the truth of a conjecture by Cameron, that these questions of the uniqueness of a certain combinatorial structure are equivalent and give an affirmative answer.
Theorem 1. Let G be a group k-homogeneous but not k-transitive on a finite set f2 of n points, where n>=2k. Then, up to permutation isomorphism, one of the following holds: (i) k = 2 and G < AFL(1,
• Mathematics
• 1965
From any given permutation group acting on a finite collection of n points one can form, for each positive integer k<=n, two permutation groups by considering respectively the permutations induced by