Tuesday, August 9, 2016 2:30 pm
-
3:20 pm
EDT (GMT -04:00)
Title: Controllable Graphs Determined by their Generalized Spectrums
Speaker: | Chen Xie |
Affiliation: | University of Waterloo |
Room: | MC 6486 |
Abstract:
A
graph
G
is
controllable
if
its
walk
matrix
$W
=
\{
1
A1
(A^2)1
...
(A^(n-1))1\}$
is
invertible.
G
is
determined
by
its
generalized
spectrum
if
for
any
graph
H,
G
and
H
are
cospectral
with
cospectral
complements
implies
that
G
and
H
are
isomorphic.
We
derive
some
exclusion conditions
on
the
arithmetic
properties
of
the
walk
matrix,
and
show
that for
all
controllable
graphs
G
whose
walk
matrix
W
satisfy
$\det(W)
\2^\floor{n/2}$
is
an
odd
square-free
integer,
G
is
determined
by
its generalized
spectrum.