๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Infinitude of 7-Arc-Transitive Graphs

โœ Scribed by Marston D.E. Conder; Cameron G. Walker

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
144 KB
Volume
208
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis

By theorems of Tutte, Weiss, and others, it is known that there are no finite symmetric graphs of degree greater than 2 with automorphism group transitive on 8-arcs, and that 7-arc-transitivity can occur only in the case of graphs of degree 3 m q 1. In this article it is shown that there are infinitely many 7-arc-transitive finite quartic graphs; indeed for all but finitely many positive integers n, there is a finite connected 7-arc-transitive quartic graph with the alternating group A acting n transitively on its 7-arcs, and another with the symmetric group S acting transin tively on its 7-arcs. The proof uses a construction involving permutation representations of a generic infinite group to produce an infinite family of finite graphs with the required properties. แฎŠ 1998 Academic Press n Petersen's graph and the complete bipartite graphs K are 3-arcn, n 619

๐Ÿ“œ SIMILAR VOLUMES

Stability of arc-transitive graphs
Stability of arc-transitive graphs
โœ David B. Surowski ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 169 KB

## Abstract The present paper investigates arcโ€transtive graphs in terms of their stability, and shows, somewhat contrary to expectations, that the property of instability is not as rare as previously thought. Until quite recently, the only known example of a finite, arcโ€transitive vertexโ€determini

On 2-Arc-Transitive Covers of Complete G
On 2-Arc-Transitive Covers of Complete Graphs
โœ Shao-fei Du; Dragan Maruลกiฤ; Adrian O Waller ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 282 KB

Regular covers of complete graphs which are 2-arc-transitive are investigated. A classification is given of all such graphs whose group of covering transformations is either cyclic or isomorphic to Z p \_Z p , where p is a prime and whose fibrepreserving subgroup of automorphisms acts 2-arc-transiti

A class of symmetric graphs with 2-arc t
A class of symmetric graphs with 2-arc transitive quotients
โœ Bin Jia; Zai Ping Lu; Gai Xia Wang ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 179 KB

Let be an X -symmetric graph admitting an X -invariant partition B on V ( ) such that B is connected and (X , 2)-arc transitive. A characterization of ( , X , B) was given in [S. Zhou Eur J Comb 23 (2002), 741-760] for the case where |B|>| (C)โˆฉB| = 2 for an arc (B, C) of B . We consider in this arti

On Graphs Admitting Arc-Transitive Actio
On Graphs Admitting Arc-Transitive Actions of Almost Simple Groups
โœ Xin Gui Fang; Cheryl E Praeger ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 217 KB

Let โŒซ be a finite connected regular graph with vertex set V โŒซ, and let G be a subgroup of its automorphism group Aut โŒซ. Then โŒซ is said to be G-locally primitiยจe if, for each vertex โฃ , the stabilizer G is primitive on the set of vertices adjacent to โฃ โฃ. In this paper we assume that G is an almost s

A Family of Non-quasiprimitive Graphs Ad
A Family of Non-quasiprimitive Graphs Admitting a Quasiprimitive 2-arc Transitive Group Action
โœ Xin Gui Fang; George Havas; Jie Wang ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 118 KB

Let be a simple graph and let G be a group of automorphisms of . The graph is (G, 2)-arc transitive if G is transitive on the set of the 2-arcs of . In this paper we construct a new family of (PSU(3, q 2 ), 2)-arc transitive graphs of valency 9 such that Aut = Z 3 .G, for some almost simple group G