c) Prove that if a plane graph G has n vertices, e edges, f faces and k components then n- e+f =k+1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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Solve 6c

6) X
Let G be a connected graph with n(G) > 2. Show that G at least 2 vertices which
are not cut-vertices of G.
For the following graph G find the following:
K(G)k' (G)
a separating set S such that |S| = K(G)
i)
ii)
c)
Prove that if a plane graph G has n vertices, e edges, f faces and k components,
then n- e+f =k+1.
Transcribed Image Text:6) X Let G be a connected graph with n(G) > 2. Show that G at least 2 vertices which are not cut-vertices of G. For the following graph G find the following: K(G)k' (G) a separating set S such that |S| = K(G) i) ii) c) Prove that if a plane graph G has n vertices, e edges, f faces and k components, then n- e+f =k+1.
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