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(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed graph with L2 edges. If G has 6 vertices every of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can have? (c) Explain the truth value for each of the following statements: (i) 4 + 3 = 6 AND 3 + 3 = 6(ii) 5 + 3 = 8 OR 3 + 1 = 5(d) Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k is a positive integer. Also estimate f(n) if f is an increasing function. (e) Show the sufficient conditions of Dirac and Ore for a graph to be Hamiltonian. Give an instance of a graph that does not satisfy Dirac's condition, but satisfies Ore's condition. (f) Measure -25 + 75 using 2's complement.
I've termed this section as Intervals of Validity since all of the illustrations will involve them. Though, there is many more to this section. We will notice a couple of theorems
how do mathematical ideas grow?
A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"
1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving
Consider the following linear equations. x1-3x2+x3+x4-x5=8 -2x1+6x2+x3-2x4-4x5=-1 3x1-9x2+8x3+4x4-13x5=49
Before we look at this, let us learn what a multiple is. Take any number say 3. Multiply this number with natural numbers. We obtain 3, 6, 9, 12, 15, 18,.........
Two trains leave the same city at the same time, one going east and the other going west. If one train is traveling at 65 mph and the other at 72 mph, how many hours will it take f
state tha different types of models used in operations research.
The population of Hamden was 350,000 in 1990. By 2000, the population had decreased to 329,000. What percent of decrease is this? First, ?nd out the number of residents who lef
The Mean Value Theorem for Integrals If f (x ) is a continuous function on [a,b] then there is a number c in [a,b] such as, ∫ b a f ( x
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