# An Edge but not Vertex Transitive Cubic Graph*

@article{Bouwer1968AnEB, title={An Edge but not Vertex Transitive Cubic Graph*}, author={I. Z. Bouwer}, journal={Canadian Mathematical Bulletin}, year={1968}, volume={11}, pages={533 - 535} }

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.

## 77 Citations

### Classifying cubic edge-transitive graphs of order 8p

- 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)…

### CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 8p2

- MathematicsBulletin 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…

### An infinite family of cubic edge- but not vertex-transitive graphs

- MathematicsDiscret. Math.
- 2004

### On Cubic Graphs Admitting an Edge-Transitive Solvable Group

- 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…

### Classifying Cubic Semisymmetric Graphs of Order 18 pn

- MathematicsGraphs Comb.
- 2014

All connected cubic semisymmetric graphs of order 18pn, where p is a prime and $${n \geq 1}$$ are classified.

### An infinite series of regular edge- but not vertex-transitive graphs

- 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…

### GRAPHS OF SMALLEST ORDERShao -

- 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…

### Bipartite edge-transitive bi-p-metacirculants

- MathematicsArs 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) .

## 2 References

### National Research Institute for Mathematical Sciences

- National Research Institute for Mathematical Sciences