# A Family of One-regular Graphs of Valency 4

@article{Marusic1997AFO, title={A Family of One-regular Graphs of Valency 4}, author={Dragan Marusic}, journal={Eur. J. Comb.}, year={1997}, volume={18}, pages={59-64} }

A graph is said to beone-regularif its automorphism group acts regularly on the set of its arcs. A construction of an infinite family of one-regular graphs of valency 4 with vertex stabilizerZ22having a non-solvable group of automorphisms is given. The smallest graph in this family has 60 vertices.

## 40 Citations

Infinitely many finite one-regular graphs of any even valency

- MathematicsJ. Comb. Theory, Ser. B
- 2004

Constructing one-regular graphs of valency 4k with non-cyclic vertex stabilizer

- MathematicsDiscret. Math.
- 2006

A Family Of Tetravalent One-Regular Graphs

- MathematicsArs Comb.
- 2017

In this paper, 4-valent one-regular graphs of order 5p, where p is a prime, are classified.

Constructing Infinite One-regular Graphs

- MathematicsEur. J. Comb.
- 1999

A construction of an infinite family of infinite one-regular graphs of valency 4 is given, which are Cayley graphs of almost abelian groups and hence of polynomial growth.

CUBIC SYMMETRIC GRAPHS OF ORDER 10p3

- Mathematics
- 2013

An automorphism group of a graph is said to be -regular if it acts regularly on the set of -arcs in the graph. A graph is -regular if its full automorphism group is -regular. In the present paper,…

Tetravalent one-regular graphs of order 2pq

- Mathematics
- 2008

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this article a complete classification of tetravalent one-regular graphs of order twice a product of two…

CUBIC SYMMETRIC GRAPHS OF ORDER 10p

- Mathematics
- 2013

. An automorphism group of a graph is said to be s -regular if it acts regularly on the set of s -arcs in the graph. A graph is s -regular if its full automorphism group is s -regular. In the present…

4-valent Graphs of Order 6p2 Admitting a Group of Automorphisms Acting Regularly on Arcs

- MathematicsArs Math. Contemp.
- 2015

The 4 -valent graphs having 6 p 2 vertices, with p a prime, are classified, admitting a group of automorphisms acting regularly on arcs, and as a corollary, the 4-valent one-regular graphs are obtained.

A classification of tetravalent one-regular graphs of order $3p^2$

- Mathematics
- 2012

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, tetravalent one-regular graphs of order 3p, where p is a prime,

## References

SHOWING 1-10 OF 12 REFERENCES

Remarks on Path-transitivity in Finite Graphs

- MathematicsEur. J. Comb.
- 1996

It is shown that if the automorphism group of a graph Γ is transitive on vertices and on undirected paths of lengthk+1 in Γ, for somek≥1, then the group is alsotransitive onk-arcs inΓ.

A one-regular graph of degree three

- Mathematics
- 1952

Soon after the publication of Tutte's paper [5] on m-cages, H. S. M. Coxeter asked in a letter to the author whether one-regular graphs of degree 3 exist. The purpose of the following paper is to…

On 4-Valent Symmetric Graphs

- MathematicsEur. J. Comb.
- 1994

This paper gives a complete classification of the graphs arising in (a) when the normal subgroup N is elementary abelian and (b), which depends to some extent on case (a), is more technical and is studied in a subsequent paper.

Constructing graphs which are ½-transitive

- MathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- 1994

Abstract An infinite family of vertex-and edge-transitive, but not arc-transitive, graphs of degree 4 is constructed.

Random Permutations: Some Group-Theoretic Aspects

- MathematicsCombinatorics, Probability and Computing
- 1993

The study of asymptotics of random permutations was initiated by Erdős and Turáan, in a series of papers from 1965 to 1968, and has been much studied since. Recent developments in permutation group…