Complement Graphs
Not what you're looking for?
(1) Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph. (Please read carefully the definition of an induced subgraph before you attempt to solve it!).
Simple graph is a graph with no loops or multiple edges. K_1 is also a tree.
(2) Let v be a cut-vertex of a simple graph G. Prove that complement(G) - v is connected. (The graph we are talking about is the complement of G with v removed.)
(By "complement (G)-v" mean "find the complement if G and remove v from it"
However, if you do it the other way , remove vfrom G and them find a complement of it (denoted then by complement (G-v),don't you get the graph?
(3) Prove or disprove: Every graph with fewer edges than vertices contains a component that is a tree.
Purchase this Solution
Solution Summary
Complement Graphs are investigated. The solution is detailed and well presented.
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
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
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.