Solution-Let g be a graph containing a cycle c

Let g be a graph containing a cycle c

Assignment Help Mathematics

Reference no: EM13926662

A. Let d ∈ N and V := {0, 1} d ; thus, V is the set of all 0-1 sequences of length d. The graph on V in which two such sequences form an edge if and only if they differ in exactly one position is called the d-dimensional cube. Determine the average degree, number of edges, diameter, girth and circumference of this graph. (Hint for the circumference: induction on d).

B. Let G be a graph containing a cycle C, and assume that G contains a path of length at least k between two vertices of C. Show that G contains a cycle of length at least √ k. Hint [1]: Consider how the path intersects C. Where can you see cycles, and can they all be short?

Reference no: EM13926662

Questions Cloud

Best describes the autocomplete function : Which of the following describes the function of the Formula Bar (as it applies to Excel 2010)?

Provide a report that data presents to exective leadership : Descriptive and inferential statistics as well as generally accepted continuous quality improvement (CQI) tools, i.e., charts, tables, and graphs, for evaluation purposes - Please provide a report that the data presents to exective leadership.

Realistic good or service for an existing industry : You will apply economic principles presented in Weeks One through Three in this week's assignment. Your assignment will be reviewed by your peers and by your facilitator in week five and should be revised as necessary based on feedback as the firs..

Calculate the after-tax component cost of capital : Calculate the after-tax component cost of capital, kc, for a 7.5 percent convertible debenture sold at par and due to mature in 25 years.

Let g be a graph containing a cycle c : The graph on V in which two such sequences form an edge if and only if they differ in exactly one position is called the d-dimensional cube. Let G be a graph containing a cycle C, and assume that G contains a path of length at least k between two ver..

Describe the envelope seal : Describe the "envelope", seal, and the early Mesopotamian writing process. Identify the issue being kept "on file," and comment on what this reveals about Mesopotamian society and the primary ways it compares to modern society in these respects.

Calculate the formula value of the right : Calculate the formula value of the right for both the rights-on and the ex-rights cases. How much is the market price of the company's stock expected to drop on the ex-rights date, all other things being equal? Why?

Testing hypotheses about variances : Question 1. A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that both are defective (a..

Identify an organized criminal enterprise : Identify an organized criminal enterprise. Research the organization's activities for the last 10-20 years and identify common "legitimate" businesses they engage in or are associated with

User Account

All Pages

Let g be a graph containing a cycle c

Reference no: EM13926662

Reference no: EM13926662

Questions Cloud

Reviews

Write a Review

Mathematics Questions & Answers

Questions on ferris wheel

Logistic map

Finding the probability of cards

Systems of ode

Derive the boolean expression

System of equations

Linear programming problem

Find the natural domain

Introduction to numerical methods

Chart of the topological manifold

Mathematics in computing

Complex problems

Assured A++ Grade

Academics

Major Subjects

Majors

Get In Touch

TERMS & POLICIES

HELP & SUPPORT