Title: Hadamard diagonalizable graphs of small order
| Speaker: | Steve Butler |
| Affiliation: | Iowa State University |
| Zoom: | Contact Sabrina Lato |
Abstract:
A
graph
whose
Laplacian
matrix
has
a
full
set
of
eigenvectors
with
entries
in
{1,-1}
is
said
to
be
Hadamard
diagonalizable
(i.e.
there
exists
a
Hadamard
matrix
which
diagonalizes
the
Laplacian
matrix).
We
demonstrate
that
the
only
diagonalizable
graphs
on
n=8k+4
vertices
are
K_n
and
K_{n/2,n/2}.
We
also
give
an
exponential
time
algorithm
that
takes
as
input
a
Hadamard
matrix
and
finds
all
graphs
which
are
diagonalized
by
that
matrix.
Using
this
all
graphs
through
order
36
which
are
Hadamard
diagonalizable
have
been
found.
This
is
joint
work
with Jane
Breen,
Steve
Butler,
Melissa
Fuentes,
Bernard
Lidický,
Michael
Phillips,
Alexander
W.
N.
Riasanovksy,
Sung-Yell
Song,
Ralihe
R.
Villagrán,
Cedar
Wiseman,
Xiaohong
Zhang.