13. Show by example that the statement "every planar graph has a vertex with degree less than or equal to 4" is false.
13. Show by example that the statement "every planar graph has a vertex with degree less than or equal to 4" is false.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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Question
Show by example that the statement “every planar graph has a vertex with degree less than or equal to 4” is false.
![### Question 13:
**Show by example that the statement "every planar graph has a vertex with degree less than or equal to 4" is false.**
In this exercise, students are asked to find an example of a planar graph where each vertex has a degree greater than 4, thereby disproving the given statement. A planar graph is a graph that can be drawn on a plane without any edges crossing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a29b20d-b628-464f-8c6e-a7e020b6af73%2F99393259-e4d3-42d6-b08e-c01eedd504b3%2Fd7svt95_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 13:
**Show by example that the statement "every planar graph has a vertex with degree less than or equal to 4" is false.**
In this exercise, students are asked to find an example of a planar graph where each vertex has a degree greater than 4, thereby disproving the given statement. A planar graph is a graph that can be drawn on a plane without any edges crossing.
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Would a segment need to be drawn between v7 & v12? Those vertices don't appear to be of degree 5.
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