1.
Consider the following graph:
e
g
i
f
h
b
d
a
c
•
How many vertices does it have?
9
•
How many edges does it have?
10
•
How many vertices of degree three does it have?
4 (
d
,
e
,
g
and
h
)
•
List the neighbors of the vertex
i
.
b
and
g
.
•
Give an example of a walk from the vertex
a
to
b
that is not a
trail.
adefhgefhb
(and other possibilities).
•
Give an example of a trail from
a
to
b
that is not a path.
There are no such trails—if a vertex
v
appears more than once in
a trail, then
v
has degree at least three, and if
v
is not the starting
or the ending vertex, then it has degree at least four. However,
the graph in the Fgure has maximum degree three, and both
a
and
b
have degree less than three.
•
Give an example of a path from
a
to
b
.
adefhb
,
adefhgib
,
adeghb
or
adegib
.
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List all cycles.
eghf
,
gibh
and
egibhf
.
•
What is the longest path this graph has as a subgraph?
adefhgib
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 Spring '09
 MarniMishna
 Vertex, vertices, Isomorphism, Longest Path

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