6,188 research outputs found
Linear groups and distance-transitive graphs
A detailed treatment is given of the graphs on which a group with simple socle PSL(n, q) acts primitively and distance-transitively
Neighbour transitivity on codes in Hamming graphs
We consider a \emph{code} to be a subset of the vertex set of a \emph{Hamming
graph}. In this setting a \emph{neighbour} of the code is a vertex which
differs in exactly one entry from some codeword. This paper examines codes with
the property that some group of automorphisms acts transitively on the
\emph{set of neighbours} of the code. We call these codes \emph{neighbour
transitive}. We obtain sufficient conditions for a neighbour transitive group
to fix the code setwise. Moreover, we construct an infinite family of neighbour
transitive codes, with \emph{minimum distance} , where this is not
the case. That is to say, knowledge of even the complete set of code neighbours
does not determine the code
Countable locally 2-arc-transitive bipartite graphs
We present an order-theoretic approach to the study of countably infinite
locally 2-arc-transitive bipartite graphs. Our approach is motivated by
techniques developed by Warren and others during the study of cycle-free
partial orders. We give several new families of previously unknown countably
infinite locally-2-arc-transitive graphs, each family containing continuum many
members. These examples are obtained by gluing together copies of incidence
graphs of semilinear spaces, satisfying a certain symmetry property, in a
tree-like way. In one case we show how the classification problem for that
family relates to the problem of determining a certain family of highly
arc-transitive digraphs. Numerous illustrative examples are given.Comment: 29 page
- …