Homogeneous factorisations of graph products

A homogeneous factorisation of a digraph consists of a partition P = {P1, . . . , Pk} of the arc set A and two vertex-transitive subgroups M G Aut() such that M fixes each Pi setwise while G leaves P invariant and permutes its parts transitively. Given two graphs 1 and 2 we consider several ways of taking a product of 1 and 2 to form a larger graph, namely the direct product, cartesian product and lexicographic product. We provide many constructions which enable us to lift homogeneous factorisations or certain arc partitions of 1 and 2, to homogeneous factorisations of the various products.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Michael Giudici, Cai Heng Li, Primoz Potocnik, Cheryl E. Praeger
• Keywords: DM 2008, Homogeneous Factorisations, Pi Setwise, Vertex-transitive Subgroups