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2. Show that each of the following graphs are not planar by finding a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (a) (b) (c) E D H 15. A E H 3 E D F G E B D B H

2. Show that each of the following graphs are not planar by finding a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (a) (b) (c) E D H 15. A E H 3 E D F G E B D B H

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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The image contains a problem statement and three graph diagrams labeled (a), (b), and (c). --- **Problem Statement:** 2. Show that each of the following graphs are not planar by finding a subgraph that is isomorphic to a subdivision of either \( K_5 \) or \( K_{3,3} \). Be sure to label the vertices! --- **Graph Diagrams:** **(a) Graph Description:** - This graph resembles a pentagon with additional internal connections. - Vertices \( A, B, C, D, \) and \( E \) form the outer pentagon. - Internal vertices are \( F, G, H, I, \) and \( J \). - Edges are drawn such that: - \( A \) is connected to \( F \) and \( B \). - \( B \) is connected to \( G \) and \( C \). - \( C \) is connected to \( H \) and \( D \). - \( D \) is connected to \( I \) and \( E \). - \( E \) is connected to \( J \) and \( A \). - The internal vertices \( J, F, G, H, I \) form a star-like shape with additional internal connections, where \( F \) is connected to \( G, H, \) and \( I\), and each pair of \( G, H, I, J\) is interconnected. **(b) Graph Description:** - This graph is structured as a 10-sided polygon with interconnections. - Outer vertices are \( A, B, C, D, E, F, G, H, I, \) and \( J \). - Internal connections form a complete inner 5-sided network between \( G, I, J, H, \) and \( F \). - Edges connect every alternate outer vertex: - i.e., \( A \) to \( C \), \( B \) to \( D \), and so on. **(c) Graph Description:** - Shaped like a square inside a square. - Outer vertices are \( A, B, G, \) and \( H \) forming a square. - Inner vertices are \( C, D, E, \) and \( F \) forming another square. - Diagonal edges cross, connecting: - \(
Transcribed Image Text:The image contains a problem statement and three graph diagrams labeled (a), (b), and (c). --- **Problem Statement:** 2. Show that each of the following graphs are not planar by finding a subgraph that is isomorphic to a subdivision of either \( K_5 \) or \( K_{3,3} \). Be sure to label the vertices! --- **Graph Diagrams:** **(a) Graph Description:** - This graph resembles a pentagon with additional internal connections. - Vertices \( A, B, C, D, \) and \( E \) form the outer pentagon. - Internal vertices are \( F, G, H, I, \) and \( J \). - Edges are drawn such that: - \( A \) is connected to \( F \) and \( B \). - \( B \) is connected to \( G \) and \( C \). - \( C \) is connected to \( H \) and \( D \). - \( D \) is connected to \( I \) and \( E \). - \( E \) is connected to \( J \) and \( A \). - The internal vertices \( J, F, G, H, I \) form a star-like shape with additional internal connections, where \( F \) is connected to \( G, H, \) and \( I\), and each pair of \( G, H, I, J\) is interconnected. **(b) Graph Description:** - This graph is structured as a 10-sided polygon with interconnections. - Outer vertices are \( A, B, C, D, E, F, G, H, I, \) and \( J \). - Internal connections form a complete inner 5-sided network between \( G, I, J, H, \) and \( F \). - Edges connect every alternate outer vertex: - i.e., \( A \) to \( C \), \( B \) to \( D \), and so on. **(c) Graph Description:** - Shaped like a square inside a square. - Outer vertices are \( A, B, G, \) and \( H \) forming a square. - Inner vertices are \( C, D, E, \) and \( F \) forming another square. - Diagonal edges cross, connecting: - \(
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