5. Let (G,) be a connected simple plane graph. Let F denote the set of faces in (G, o) and for f € F, (f) denote the length of f. Prove that Στενισ) (d(v) – 6) + 2Σ,er(((f) – 3) = -12. vEV(G) (Hint: Use Euler's Formula.)
5. Let (G,) be a connected simple plane graph. Let F denote the set of faces in (G, o) and for f € F, (f) denote the length of f. Prove that Στενισ) (d(v) – 6) + 2Σ,er(((f) – 3) = -12. vEV(G) (Hint: Use Euler's Formula.)
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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Transcribed Image Text:5. Let (G, o) be a connected simple plane graph. Let F denote the set of faces in (G, o) and for fe F,
(f) denote the length of f. Prove that
Στενις (d(v) – 6) + 2Σ,cr((f) – 3) = -12.
vEV(G)
(Hint: Use Euler's Formula.)
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