Abelian Homegeneous Factorisations of Graphs

Abstract

Abstract:A homogeneous factorisation of a graph Г is a partition of its arc set such that there exist vertex transitive subgroups M<G≤Aut(Г) such that M fixes each part setwise of the partition and Gpreserves the partition and transitive permuting the parts. In the present paper, we study homogeneous factorisation with M abelian. We give some interesting characterizations and constructions of such factorisations.