MODULE
SIX
PROBLEM
SET
1
P
ROBLEM
1
For
parts
(a)
and
(b),
indicate
if
each
of
the
two
graphs
are
equal.
Justify
your
answer.
(a)
Figure
1:
Left:
An
undirected
graph
has
5
vertices.
The
vertices
are
arranged
in
the
form
of
an
inverted
pentagon.
From
the
top
left
vertex,
moving
clockwise,
the
vertices
are
labeled:
a,
b,
c,
d,
and
e.
Undirected
edges,
line
segments,
are
between
the
following
vertices:
a
and
b;
a
and
c;
b
and
c;
c
and
d;
e
and
d;
and
e
and
c.
Figure
2:
Right:
The
adjacency
list
representation
of
a
graph.
The
list
shows
all
the
vertices,
a
through
e,
in
a
column
from
top
to
bottom.
The
adjacent
vertices
for
each
vertex
in
the
column
are
placed
in
a
row
to
the
right
of
the
corresponding
vertex’s
cell
in
the
column.
An
arrow
points
from
each
cell
in
the
column
to
its
corresponding
row
on
the
right.
Data
from
the
list,
as
follows:
Vertex
a
is
adjacent
to
vertices
b
and
c.
Vertex
b
is
adjacent
to
vertices
a
and
c.
Vertex
c
is
adjacent
to
vertices
a,
b,
d,
and
e.
Vertex
d
is
adjacent
to
vertices
c
and
e.
Vertex
e
is
adjacent
to
vertices
c
and
d.
The
provided
adjacency
list
tells
us
which
vertices
are
connected
together.
The
graph
that
corresponds
to
this
adjacency
list
will
look
like
this and this graph is equal to the one that is present on
the left the in
question.
Therefore,
the
2
graphs
are
considered
to
be
equal.
(b)
Figure
3:
An
undirected
graph
has
5
vertices.
The
vertices
are
arranged
