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5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)

5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)

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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5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)
Transcribed Image Text:5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)
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