# An Edge but not Vertex Transitive Cubic Graph*

```@article{Bouwer1968AnEB,
title={An Edge but not Vertex Transitive Cubic Graph*},
author={I. Z. Bouwer},
year={1968},
volume={11},
pages={533 - 535}
}```
• I. Bouwer
• Published 1 October 1968
• Mathematics
Let G be an undirected graph, without loops or multiple edges. An automorphism of G is a permutation of the vertices of G that preserves adjacency. G is vertex transitive if, given any two vertices of G, there is an automorphism of the graph that maps one to the other. Similarly, G is edge transitive if for any two edges (a, b) and (c, d) of G there exists an automorphism f of G such that {c, d} = {f(a), f(b)}. A graph is regular of degree d if each vertex belongs to exactly d edges.
• Mathematics
• 2009
A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman (J. Combin. Theory3 (1967) 215–232)
• Mathematics
Bulletin of the Australian Mathematical Society
• 2008
Abstract A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman [J. Folkman, ‘Regular
• Mathematics
• 2004
Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every
• Mathematics
Graphs Comb.
• 2014
All connected cubic semisymmetric graphs of order 18pn, where p is a prime and \$\${n \geq 1}\$\$ are classified.
• Mathematics
• 2002
Let n be an integer and q be a prime power. Then for any 3 ≤ n ≤ q-1, or n=2 and q odd, we construct a connected q-regular edge-but not vertex-transitive graph of order 2qn+1. This graph is defined
• Mathematics
• 2007
A regular and edge-transitive graph which is not vertex-transitive is said to be semisymmetric. Every semisymmetric graph is necessarily bipartite, with the two parts having equal size and the
• Mathematics
Ars Math. Contemp.
• 2019
It is proved that if G is a Sylow p -subgroup in the full automorphism group Aut(Γ) of a graph Γ, then G is normal in Aut( Γ) .

### National Research Institute for Mathematical Sciences

• National Research Institute for Mathematical Sciences