Title: The spectral radius of graphs with no odd wheels
| Speaker: | Dheer Noal Desai |
| Affiliation: | University of Delaware |
| Zoom: | Contact Soffia Arnadottir |
Abstract:
The
odd
wheel
W_{2k+1}
is
the
graph
formed
by
joining
a
vertex
to
a
cycle
of
length
2k.
In
this
talk,
we
will
investigate
the
largest
value
of
the
spectral
radius
of
the
adjacency
matrix
of
an
n-vertex
graph
that
does
not
contain
W_{2k+1}.
We
determine
the
structure
of
the
spectral
extremal
graphs
for
all
k
geq
2,
k
not
equal
to
4
and
5.
When
k=2,
we
show
that
these
spectral
extremal
graphs
are
among
the
Tur\'an-extremal
graphs
on
n
vertices
that
do
not
contain
W_{2k+1}
and
have
the
maximum
number
of
edges,
but
when
k
geq
9,
we
show
that
the
family
of
spectral
extremal
graphs
and
the
family
of
Tur\'an-extremal
graphs
are
disjoint.
We
will
give
an
overview
of
similar
results
and
describe
a
method
that
may
help
us
find
new
ones.
This
is
joint
work
with
Sebastian
Cioaba
(University
of
Delaware)
and
Michael
Tait
(Villanova
University).