The girth of a graph is defined as the length of a shortest cycle contained in the graph. Show that if G = (V, E) is a connected planar graph with girth g (where g 2 3), then m < (n2) where n = m = |E|. V] and %3D 9-2 %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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QUESTION 4
The girth of a graph is defined as the length of a shortest cycle contained in the graph. Show that if
G = (V, E) is a connected planar graph with girth g (where g 2 3), then m <
m = |E|.
g(n-2)
9-2
where n =
|V] and
Transcribed Image Text:QUESTION 4 The girth of a graph is defined as the length of a shortest cycle contained in the graph. Show that if G = (V, E) is a connected planar graph with girth g (where g 2 3), then m < m = |E|. g(n-2) 9-2 where n = |V] and
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