Connectivity and matching properties of distance-regular graphs
| Speaker: | Sebi Ciaoba |
|---|---|
| Affiliation: | University of Delaware |
| Room: | Mathematics and Computer Building (MC) 5158 |
Abstract:
A
strongly
regular
graph
is
a
regular
graph
such
that
the
size
of
the
common
neighborhood
of
two
distinct
vertices
depends
only
on
whether
the
vertices
are
adjacent
or
not.
A
primitive
strongly
regular
graph
is
a
strongly
regular
graph
that
is
not
a
union
of
cliques
or
a
complete
multipartite
graph.
The
second
subconstituent
of
a
strongly
regular
graph
G
with
respect
to
a
vertex
x,
is
the
subgraph
of
G
induced
by
the
vertices
at
distance
2
from
x.
An
important
property
of
primitive
strongly
regular
graphs
is
the
fact
that
the
second
subconstituent
of
any
vertex
is
connected.
In
2011,
at
GAC5,
Andries
Brouwer
asked
to
what
extent
can
this
statement
be
generalized
to
distance-regular
graphs?
I
will
discuss
our
progress
on
this
problem.
This
is
joint
work
with
Jack
Koolen.
A
graph
is
called
t-extendable
if
it
has
even
order
and
any
matching
of
size
t
is
contained
in
a
perfect
matching.
The
extendability
of
a
graph
is
the
maximum
t
such
that
the
graph
is
t-extendable.
In
1980s,
Holton
studied
the
extendability
of
strongly
regular
graphs.
I
will
present
some
recent
results
regarding
the
extendability
of
strongly
regular
graphs
and
distance-regular
graphs.
This
is
joint
work
with
Jack
Koolen
and
Weiqiang
Li.