4 research outputs found
On commutative association schemes and associated (directed) graphs
Let denote the Bose--Mesner algebra of a commutative -class
association scheme (not necessarily symmetric), and
denote a (strongly) connected (directed) graph with adjacency matrix . Under
the assumption that belongs to , in this paper, we describe the
combinatorial structure of .
Among else, we show that, if is a commutative -class
association scheme that is not an amorphic symmetric scheme, then we can always
find a (directed) graph such that the adjacency matrix of
generates the Bose--Mesner algebra of