Parallelism

EnProblems involving the idea of parallelism occur in finite geometry and in graph theory. This article addresses the question of constructing parallelisms with some degree of "symmetry". In particular, can we say anything on parallelisms admitting an automorphism group acting doubly transitively on "parallel classes"

On classifying finite edge colored graphs with two transitive automorphism groups

This paper classifies all finite edge colored graphs with doubly transitive automorphism groups. This result generalizes the classification of doubly transitive balanced incomplete block designs with λ=1 and doubly transitive one-factorizations of complete graphs. It also provides a classification of all doubly transitive symmetric association schemes

SGDs with doubly transitive automorphism group

Symmetric graph designs, or SGDs, were defined by Gronau et al. as a common generalization of symmetric BIBDs and orthogonal double covers. This note gives a classification of SGDs admitting a 2-transitive automorphism group. There are too many for a complete determination, but in some special cases the determination can be completed, such as those that admit a 3-transitive group, and those with λ = 1. The latter case includes the determination of all near 1-factorizations of Kn (partitions of the edge set into subsets each of which consists of disjoint edges covering all but one point), which admit 2-transitive groups.</p

SGDs with doubly transitive automorphism group

Symmetric graph designs, or SGDs, were defined by Gronau et al. as a common generalization of symmetric BIBDs and orthogonal double covers. This note gives a classification of SGDs admitting a 2-transitive automorphism group. There are too many for a complete determination, but in some special cases the determination can be completed, such as those that admit a 3-transitive group, and those with λ = 1. The latter case includes the determination of all near 1-factorizations of Kn (partitions of the edge set into subsets each of which consists of disjoint edges covering all but one point), which admit 2-transitive groups.</p