Tuesday, May 31, 2016 3:30 pm
-
4:30 pm
EDT (GMT -04:00)
Title: Inverses of Trees
| Speaker: | krystal Guo |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
We
consider
trees
whose
adjacency
matrix
are
invertible
matrices.
A
classic
result
of
Godsil
gives
that
the
inverses
of
an
invertible
tree
T
corresponds
to
a
graph
which
contains
T
as
a
spanning
tree.
This
allows
for
the
characterization
of
the
invertible
trees
which
attain
the
minimum
and
maximum
median
eigenvalue
by
Godsil
and
Zhang
&
Chang,
respectively.
We
give
an
alternative
proof
for
the
characterization
of
trees
with
maximum
median
eigenvalue
and,
in
doing
so,
define
a
poset
on
the
set
of
invertible
trees
on
2n
vertices.