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Problem 1: Determine whether graphs G and H are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski's theorem. Graph G: Graph H: g

Problem 1: Determine whether graphs G and H are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski's theorem. Graph G: Graph H: g

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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**Problem 1:** Determine whether graphs \( G \) and \( H \) are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski’s theorem. **Graph G:** - The graph contains seven vertices labeled \( a, b, c, d, e, f, g \). - Edges connect the following pairs of vertices: - \( a \) to \( c, e, d, g \) - \( b \) to \( c, d, e, f, g \) - \( c \) to \( f \) - \( d \) to \( f \) - \( e \) to \( f, g \) - \( g \) to \( f \) **Graph H:** - The graph contains seven vertices labeled \( a, b, c, d, e, f, g \). - Edges connect the following pairs of vertices: - \( a \) to \( b, c, f, g \) - \( b \) to \( c, d, e, f \) - \( c \) to \( d, f \) - \( d \) to \( e \) - \( e \) to \( f, g \) - \( f \) to \( g \) To determine planarity, consider if you can redraw the graph on a plane without edges crossing. If a graph cannot be drawn as such, use Kuratowski's theorem, which states that a graph is non-planar if it contains a subgraph homeomorphic to \( K_5 \) (complete graph on five vertices) or \( K_{3,3} \) (complete bipartite graph on six vertices, divided into two sets of three).
Transcribed Image Text:**Problem 1:** Determine whether graphs \( G \) and \( H \) are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski’s theorem. **Graph G:** - The graph contains seven vertices labeled \( a, b, c, d, e, f, g \). - Edges connect the following pairs of vertices: - \( a \) to \( c, e, d, g \) - \( b \) to \( c, d, e, f, g \) - \( c \) to \( f \) - \( d \) to \( f \) - \( e \) to \( f, g \) - \( g \) to \( f \) **Graph H:** - The graph contains seven vertices labeled \( a, b, c, d, e, f, g \). - Edges connect the following pairs of vertices: - \( a \) to \( b, c, f, g \) - \( b \) to \( c, d, e, f \) - \( c \) to \( d, f \) - \( d \) to \( e \) - \( e \) to \( f, g \) - \( f \) to \( g \) To determine planarity, consider if you can redraw the graph on a plane without edges crossing. If a graph cannot be drawn as such, use Kuratowski's theorem, which states that a graph is non-planar if it contains a subgraph homeomorphic to \( K_5 \) (complete graph on five vertices) or \( K_{3,3} \) (complete bipartite graph on six vertices, divided into two sets of three).
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