TY - JOUR
T1 - Homogeneous factorisations of graph products
AU - Giudici, Michael
AU - Li, Cai-Heng
AU - Potocnik, P.
AU - Praeger, Cheryl
PY - 2008
Y1 - 2008
N2 - A homogeneous factorisation of a digraph Γ consists of a partition P={P1, ... , PK} of the arc set AΓ and two vertex-transitive subgroups M≤G≤Aut(Γ) such that M fixes each Pi setwise while G leaves P invariant and permutes its parts transitively. Given two graphs Γ1 and Γ2 we consider several ways of taking a product of Γ1 and Γ2 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 Γ1 and Γ2, to homogeneous factorisations of the various products.\
AB - A homogeneous factorisation of a digraph Γ consists of a partition P={P1, ... , PK} of the arc set AΓ and two vertex-transitive subgroups M≤G≤Aut(Γ) such that M fixes each Pi setwise while G leaves P invariant and permutes its parts transitively. Given two graphs Γ1 and Γ2 we consider several ways of taking a product of Γ1 and Γ2 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 Γ1 and Γ2, to homogeneous factorisations of the various products.\
U2 - 10.1016/j.disc.2007.07.025
DO - 10.1016/j.disc.2007.07.025
M3 - Article
SN - 0012-365X
VL - 308
SP - 3652
EP - 3667
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 16
ER -