74 research outputs found
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"
Brick assignments and homogeneously almost self-complementary graphs
AbstractA graph is called almost self-complementary if it is isomorphic to the graph obtained from its complement by removing a 1-factor. In this paper, we study a special class of vertex-transitive almost self-complementary graphs called homogeneously almost self-complementary. These graphs occur as factors of symmetric index-2 homogeneous factorizations of the âcocktail party graphsâ K2nânK2. We construct several infinite families of homogeneously almost self-complementary graphs, study their structure, and prove several classification results, including the characterization of all integers n of the form n=pr and n=2p with p prime for which there exists a homogeneously almost self-complementary graph on 2n vertices
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
Primitive one-factorizations and the geometry of mixed translations
AbstractWe construct an infinite family of one-factorizations of Kv admitting an automorphism group acting primitively on the set of vertices but no such group acting doubly transitively. We also give examples of one-factorizations which are live, in the sense that every one-factor induces an automorphism, but do not coincide with the affine line parallelism of AG(n,2). To this purpose we develop the notion of a âmixed translationâ in AG(n,2)
All totally symmetric colored graphs
In this paper we describe all edge-colored graphs that are fully symmetric
with respect to colors and transitive on every set of edges of the same color.
They correspond to fully symmetric homogeneous factorizations of complete
graphs. Our description completes the work done in our previous paper, where we
have shown, in particular, that there are no such graphs with more than 5
colors. Using some recent results, with a help of computer, we settle all the
cases that was left open in the previous paper.Comment: 13 page
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