Petersen Graph
Not what you're looking for?
Show that the Petersen graph is nonplanar by
a) showing that it has k3,3 as a subcontraction, and
b) using the problem 1 show above part a)
You don't have to solve problem 1.
Can you explain about contraction.
problem 1.-Let k>=3 be an integer , and let G be a plane graph of order n(>=k) and size m.
a) If the length of every cycle is at least k, then determine an upper bound B for m in terms of n and k.
b)Show that the bound B obtained in a) is sharp by determining for arbitrary k>=3, a plane graph G of order n and size B, every cycle of which has length at least k.
Note: if a planar graph is embedded in the plane ,then it is called a plane graph.
keywords: peterson graph
Purchase this Solution
Solution Summary
The Petersen Graph is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Show that the Petersen graph is nonplanar by
a) showing that it has k3,3 as a subcontraction, and
Let X={1,2,3} and Y={4,5,6}, we can re-draw the above Petersen graph as follows.
So, it is clear that Petersen graph has ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.