2 research outputs found
Unification of graph products and compatibility with switching
We define the type of graph products, which enable us to treat many graph
products in a unified manner. These unified graph products are shown to be
compatible with Godsil--McKay switching. Furthermore, by this compatibility, we
show that the Doob graphs can also be obtained from the Hamming graphs by
switching
The Terwilliger algebra of the twisted Grassmann graph: the thin case
The Terwilliger algebra of a finite connected simple graph
with respect to a vertex is the complex semisimple matrix algebra generated
by the adjacency matrix of and the diagonal matrices
, where denotes the
characteristic vector of the set of vertices at distance from . The
twisted Grassmann graph discovered by Van Dam and Koolen
in 2005 has two orbits of the automorphism group on its vertex set, and it is
known that one of the orbits has the property that is thin whenever
is chosen from it, i.e., every irreducible -module satisfies for all . In this paper, we determine all the
irreducible -modules of for this "thin" case.Comment: 22 page