Finally applying the same argument one more time we conclude that
the Euler characteristic of
G
is one less than the sum of the Euler
characteristics of
G
123
and
G
4
. Thus
G
has Euler characteristic 4+2

1 = 5.
(3)
is
True
.
Suppose that a connected planar graph with 6 edges
splits the plane into 7 regions. The Euler characteristic of this graph
is
V

6 + 7 =
V
+ 1 by definition. BUt by the Euler characteristic
theorem the euler characteristic of the graph must be equal to 2. So
V
= 1.
The correct answer is
(c)
.
square
16
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 Spring '08
 schneps
 Math, Planar graph, Euler

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