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2. Euler's theorem for a connected planar graph G states that we + r = 2, were v, e, r represent the order, size, and number of regions of G when drawn in the plane without edge crossings. Suppose that a planar graph has order v, size e, 7 regions, and c components. What equation gives the relationship among the parameters v, e, r, c? Prove your answer.

2. Euler's theorem for a connected planar graph G states that we + r = 2, were v, e, r represent the order, size, and number of regions of G when drawn in the plane without edge crossings. Suppose that a planar graph has order v, size e, 7 regions, and c components. What equation gives the relationship among the parameters v, e, r, c? Prove your answer.

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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2. Euler's theorem for a connected planar graph G states that ve + r = 2, were v, e, r represent the order, size, and number of regions of G when drawn in the plane without edge crossings. Suppose that a planar graph has order v, size e, 7 regions, and c components. What equation gives the relationship among the parameters v, e, r, c? Prove your answer.
Transcribed Image Text:2. Euler's theorem for a connected planar graph G states that ve + r = 2, were v, e, r represent the order, size, and number of regions of G when drawn in the plane without edge crossings. Suppose that a planar graph has order v, size e, 7 regions, and c components. What equation gives the relationship among the parameters v, e, r, c? Prove your answer.
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