Product constructions for transitive decompositions of graphs
نویسنده
چکیده
A decomposition of a graph is a partition of the edge set, giving a set of subgraphs. A transitive decomposition is a decomposition which is highly symmetrical, in the sense that the subgraphs are preserved and transitively permuted by a group of automorphisms of the graph. This paper describes some ‘product’ constructions for transitive decompositions of graphs, and shows how these may be used to characterise transitive decompositions where the group has a particular type of rank 3 action on the graph.
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Transitive decompositions of graph products: rank 3 grid type
A transitive decomposition is a pair ðG;PÞ where G is a graph and P is a partition of the arc set of G, such that there exists a group of automorphisms of G which leaves P invariant and transitively permutes the parts in P. This paper concerns transitive decompositions where the group is a primitive rank 3 group of ‘grid’ type. The graphs G in this case are either products or Cartesian products...
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