2-Arc-transitive Cayley graphs on alternating groups
Jiangmin Pan, Binzhou Xia, Fugang Yin

TL;DR
This paper investigates 2-arc-transitive Cayley graphs on alternating groups, characterizing their automorphism groups and constructing an infinite family of such graphs with specific properties.
Contribution
It provides a complete characterization of automorphism groups of 2-arc-transitive Cayley graphs on alternating groups and constructs the first infinite family of such graphs.
Findings
Automorphism groups have socle either A_{n+1} or A_{n+2}.
Constructed the first infinite family of (A_{n+2},2)-arc-transitive Cayley graphs on A_n.
Extended understanding of symmetry properties of Cayley graphs on alternating groups.
Abstract
An interesting fact is that most of the known connected -arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are -arc-transitive Cayley graphs on . This motivates the study of -arc-transitive Cayley graphs on for arbitrary valency. In this paper, we characterize the automorphism groups of such graphs. In particular, we show that for a non-complete -arc-transitive Cayley graph on with almost simple, the socle of is either or . We also construct the first infinite family of -arc-transitive Cayley graphs on .
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Geometric and Algebraic Topology
