Let G be a simple plane graph with fewer than 12 faces, in which each vertex has degree at least 3. (i) Use Euler's formula to prove that G has a face bounded by at most four edges. (ii) Give an example to show that the result of part (i) is false if G has 12 faces.
Let G be a simple plane graph with fewer than 12 faces, in which each vertex has degree at least 3. (i) Use Euler's formula to prove that G has a face bounded by at most four edges. (ii) Give an example to show that the result of part (i) is false if G has 12 faces.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 74EQ
Related questions
Question
Answer for # 17 please
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning