Homogeneous factorisations of graph products
نویسندگان
چکیده
منابع مشابه
Homogeneous factorisations of graph products
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 6 G 6 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, cartes...
متن کاملHomogeneous factorisations of Johnson graphs
For a graph Γ, subgroups M < G 6 Aut(Γ), and an edge partition E of Γ, the pair (Γ, E) is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of E , while G permutes the parts of E transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite families and nine sporadic examples.
متن کاملHomogeneous factorisations of complete multipartite graphs
A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M < G 6 Aut(Γ) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M acts regularly on vertices. We provide a necessary ...
متن کاملHomogeneous factorisations of graphs and digraphs
A homogeneous factorisation (M,G,Γ,P) is a partition P of the arc set of a digraph Γ such that there exist vertex transitive groups M < G 6 Aut(Γ) such that M fixes each part of P setwise while G acts transitively on P. Homogeneous factorisations of complete graphs have previously been studied by the second and fourth authors, and are a generalisation of vertex-transitive self-complementary dig...
متن کاملHomogeneous factorisations of complete graphs with edge-transitive factors
A factorisation of a complete graph Kn is a partition of its edges with each part corresponding to a spanning subgraph (not necessarily connected), called a factor. A factorisation is called homogeneous if there are subgroups M <G ≤ Sn such that M is vertex-transitive and fixes each factor setwise, and G permutes the factors transitively. We classify the homogeneous factorisations of Kn for whi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.07.025