# On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order

On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with... Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p k (k≥1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer A v of a vertex v in A is a 2-group if p ≠ 5, or a {2,3}-group if p = 5. Furthermore, if p = 5 |A v | is not divisible by 32. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p k (k≥1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order

, Volume 19 (1) – Jan 1, 2003
4 pages

/lp/springer-journals/on-the-stabilizer-of-the-automorphism-group-of-a-4-valent-vertex-cAilSYFwA0
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-003-0083-5
Publisher site
See Article on Publisher Site

### Abstract

Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p k (k≥1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer A v of a vertex v in A is a 2-group if p ≠ 5, or a {2,3}-group if p = 5. Furthermore, if p = 5 |A v | is not divisible by 32. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p k (k≥1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2003

### References

Access the full text.