29 research outputs found
Notes on the connectivity of Cayley coset digraphs
Hamidoune's connectivity results for hierarchical Cayley digraphs are
extended to Cayley coset digraphs and thus to arbitrary vertex transitive
digraphs. It is shown that if a Cayley coset digraph can be hierarchically
decomposed in a certain way, then it is optimally vertex connected. The results
are obtained by extending the methods used by Hamidoune. They are used to show
that cycle-prefix graphs are optimally vertex connected. This implies that
cycle-prefix graphs have good fault tolerance properties.Comment: 15 page
Connectivite des graphes de cayley abeliens sans K4
AbstractWe give a description for the class of connected Abelian Cayley digraphs containing no K4 with connectivity less than the outdegree. We show that no member of this class is anti-symmetric
A Structure Theorem for Small Sumsets in Nonabelian Groups
Let G be an arbitrary finite group and let S and T be two subsets such that
|S|>1, |T|>1, and |TS|< |T|+|S|< |G|-1. We show that if |S|< |G|-4|G|^{1/2}+1
then either S is a geometric progression or there exists a non-trivial subgroup
H such that either |HS|< |S|+|H| or |SH| < |S|+|H|. This extends to the
nonabelian case classical results for Abelian groups. When we remove the
hypothesis |S|<|G|-4|G|^{1/2}+1 we show the existence of counterexamples to the
above characterization whose structure is described precisely.Comment: 23 page