Abelian permutation groups with graphical representations

2019/10/25 by Grech, Mariusz, Kisielewicz, Andrzej
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.11816

Abstract

In this paper we characterize permutation groups that are automorphism groups of coloured graphs and digraphs and are abelian as abstract groups. This is done in terms of basic permutation group properties. Using Schur's classical terminology, what we provide is characterizations of the classes of 2-closed and 2*-closed abelian permutation groups. This is the first characterization concerning these classes since they were defined.

Related

• Graphical Cyclic Permutation Groups
• Decompositions of the authomorphism groups of edge-colored graphs into the direct product of permutation groups
• Automorphism groups of graphs
• Graphs, permutations and topological groups
• Automorphism Groups of Geometrically Represented Graphs