Can I read Corrigendum to “On 2-arc-transitivity of Cayley graphs” [J. Combin. Theory Ser. B 87 (2003) 162–196] on EtoBox?

Corrigendum to “On 2-arc-transitivity of Cayley graphs” [J. Combin. Theory Ser. B 87 (2003) 162–196] by Dragan Marušič is a Computer Science article available to read on EtoBox.

What is Corrigendum to “On 2-arc-transitivity of Cayley graphs” [J. Combin. Theory Ser. B 87 (2003) 162–196] about?

A characterization of 2-arc-transitive dihedrants, that is, Cayley graphs of dihedral groups, is given in [3, Theorem 8.4], describing such graphs either explicitly or as cyclic covers of certain basic dihedrants. The proof is carried out via a reduction scheme based on the classical results due to Schur and Wielandt, saying that cyclic groups of composite order and dihedral groups are all B-groups [4, Theorems 25.3 and 25.6]. Consequently, the automorphism group A of a connected 2-arc-transitive Cayley graph X K 2n of a dihedral group D 2n = ρ, τ | ρ n = τ 2 = (ρτ ) 2 = 1 is necessarily imprimitive, allowing the above mentioned reduction with respect to blocks of minimal length. The various possibilities that may occur for such blocks are covered in [3,]. Unfortunately, in Lemma 7.2 (and consequently in Lemma 7.3) one of the cases needed to be considered was missed out. This case essentially leads to the situation, where the group A has an imprimitivity block system with blocks of size 2 having nonempty intersection with both orbits of ρ, and a single edge between any two adjacent blocks. In this note we fill out the gap by proving a new lemma (Lemma 3 below) taking care of this c

Who reads Corrigendum to “On 2-arc-transitivity of Cayley graphs” [J. Combin. Theory Ser. B 87 (2003) 162–196]?

Author

Dragan Marušič

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0095-8956)

Published

2006

Language

EN

Field

Computer Science (Physical Sciences)