Automorphism groups of Cayley graphs generated by block transpositions and regular Cayley maps
Annachiara Korchmaros, Istv\'an Kov\'acs

TL;DR
This paper characterizes the automorphism group of Cayley graphs generated by block transpositions, revealing a structure involving dihedral groups and exploring implications for regular Cayley maps with bioinformatics relevance.
Contribution
It proves that the automorphism group of these Cayley graphs is a product of left translations and a dihedral group, and analyzes related subgraphs and Cayley maps.
Findings
Automorphism group is the product of left translation group and dihedral group D_{n+1}.
Subgraph induced by block transpositions has a dihedral automorphism group.
Identifies a connection between cyclic subgroups and regular Cayley maps on Sym_n.
Abstract
This paper deals with the Cayley graph where the generating set consists of all block transpositions. A motivation for the study of these particular Cayley graphs comes from current research in Bioinformatics. As the main result, we prove that Aut is the product of the left translation group by a dihedral group of order . The proof uses several properties of the subgraph of induced by the set . In particular, is a -regular graph whose automorphism group is has as many as maximal cliques of size and its subgraph whose vertices are those in these cliques is a -regular, Hamiltonian, and vertex-transitive graph. A relation of the unique cyclic subgroup of …
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