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(b) Let G be a plane graph, and let c(G) be the number of components of G. State a generalisation of Euler's Formula that describes the relationship between v(G), e(G), f(G) and c(G). Prove this generalisation.

(b) Let G be a plane graph, and let c(G) be the number of components of G. State a generalisation of Euler's Formula that describes the relationship between v(G), e(G), f(G) and c(G). Prove this generalisation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) please

1. Recall that Euler's formula (as we saw in lectures as Theorem 5.5) concerns connected plane graphs. (a) Give an example to demonstrate that Euler's formula does not hold if G is not connected. (b) Let G be a plane graph, and let c(G) be the number of components of G. State a generalisation of Euler's Formula that describes the relationship between v(G), e(G), ƒ(G) and c(G). Prove this generalisation.
Transcribed Image Text:1. Recall that Euler's formula (as we saw in lectures as Theorem 5.5) concerns connected plane graphs. (a) Give an example to demonstrate that Euler's formula does not hold if G is not connected. (b) Let G be a plane graph, and let c(G) be the number of components of G. State a generalisation of Euler's Formula that describes the relationship between v(G), e(G), ƒ(G) and c(G). Prove this generalisation.
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