Let G be a connected graph and e and edge of G. Prove that k(G) = k(G - e) + k(G/e). Here k(G) represents the number of spanning trees ofG and G-e and G/e are obtained from G by deleting edge e and contracting edge e, respectively.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let G be a connected graph and e and edge of G. Prove that
k(G) = k(G – e)+ k(G/e).
Here k(G) represents the number of spanning trees of G and G-
G by deleting edge e and contracting edge e, respectively.
%3D
and G/e are obtained from
Transcribed Image Text:Let G be a connected graph and e and edge of G. Prove that k(G) = k(G – e)+ k(G/e). Here k(G) represents the number of spanning trees of G and G- G by deleting edge e and contracting edge e, respectively. %3D and G/e are obtained from
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