Hamiltonian and nonhamiltonian graphs

Assignment Help Mathematics

Reference no: EM13123371

Show that this theorem 1 is sharp, that is, show that for infinitely many n>=3 there are non-hamiltonian graphs G of order n such that degu+degv>=n-1 for all distinct nonadjacent u and v.

Can you explain this theorem,please

Theorem1: If G is a graph of order n>=3 such that for all distinct nonadjacent vertices u and v, deg v +deg u >=n then G is hamiltonian.

Can you explain it step by step and draw a graph.

Reference no: EM13123371

Questions Cloud

Illustrate what was the original cost of the copier to john : Assuming the computer has an eleven-year life and will have no salvage value atthe expiration of the lease, illustrate what was the original cost of the copier to John? (b) What amountwould each payment be if the 11 annual payments are to be made ..

What the oxidation state of br2 : what the oxidation state P in PO4^-2? what the oxidation state O in PO4^-2?

Find probability that if company books seats not available : The booked passengers actually arrive for the flight. Estimate the probability that if the company books 278 persons. not enough seats will be available.

Aftertax cash flow from the sale : If the relevant tax rate is 34 percent, what is the aftertax cash flow from the sale of this asset? (Do not round your intermediate calculations.)

Hamiltonian and nonhamiltonian graphs : Show that this theorem 1 is sharp, that is, show that for infinitely many n>=3 there are non-hamiltonian graphs G of order n such that degu+degv>=n-1 for all distinct nonadjacent u and v.

Calculate the molarity of each of the given solutions : Calculate the molarity of each of the following solutions. (a) 23.0 g of ethanol (C2H5OH) in 545 mL of solution (b) 15.4 g of sucrose (C12H22O11) in 74.0 mL of solution

Highlighting the part indicated by given interval : Find a definite integral that represents the arc length of the curve over the indicated interval and observe that the length cannot be evaluated with the techniques studied so far

How to conclude proportion has indeed changed : School seniors in his random sample, 159 believe that "getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed?

What is the molarity of a solution of vinegar : What is the molarity of a solution of vinegar that is 5.00 % by mass acetic acid (CH3CO2H) and has a density of 1.01 g/mL.

User Account

All Pages