Spreads Admitting Regular Elliptic Covers

Cyclic elliptic spreads

Moderately large numbers of transitive elliptic spreads are constructed in characteristic 2 and dimension ≡ 2 (mod 4).

Regular Difference Covers

Spreads in Strongly Regular Graphs

A spread of a strongly regular graph is a partition of the vertex set into cliques that meet Delsarte's bound (also called Hoffman's bound). Such spreads give rise to colorings meeting Hoffman's lower bound for the chromatic number and to certain imprimitive three-class association schemes. These correspondences lead to conditions for existence. Most examples come from spreads and fans in (part...

On dihedrants admitting arc-regular group actions

We consider Cayley graphs Γ over dihedral groups, dihedrants for short, which admit an automorphism group G acting regularly on the arc set of Γ . We prove that, if D2n ≤G≤ Aut(Γ ) is a regular dihedral subgroup of G of order 2n such that any of its index 2 cyclic subgroups is core-free in G, then Γ belongs to the family of graphs of the form (Kn1 ⊗ · · · ⊗Kn )[Kc m], where 2n= n1 · · ·n m, and...

Regular clique covers of graphs

A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect in exactly p vertices. A graph G is said to have a p-regular k-clique cover if there is a p-regular family H of k-cliques of G such that each edge of G belongs to a clique in H. Such a p-regular kclique cover is separable if the complete subgraphs of order p that arise as intersections of pairs o...