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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.
Euler''''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
Concrete to Abstract : Mathematics, like all human knowledge, grows out of our concrete experiences. Let us take the example of three-dimensional shapes. Think about how you came
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Verify the Parseval theorem for the discrete-time signal x(n) and its DFT from given equations. Compute the linear convolution of the discrete-time signal x(n) ={3, 2, 2,1} and
Two angles are complementary. The larger angle is 15° more than twice the smaller. Find out the measure of the smaller angle. Let x = the number of degrees in the smaller angle
The scores of students taking the ACT college entrance examination are normally distributed with a mean µ = 20.1 and a standard deviation σ = 5.8. a) A single student is sele
Multistage sampling Multistage sampling is similar to stratified sampling except division is done on geographical/location basis, for illustration a country can be divided into
HOW MUCH WILL A NEW CAR COST? THE AVERAGE COST OF A NEW CAR IN 1990 WAS $14371. IN 2003 THE AVERAGE COST HAD RISEN TO $22360. WHAT IS THE AMOUNT OF THE MONTHLY PAYMENT? THE AMOUNT
10000+9854
Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:
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