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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.
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Finding the Equation of a line, Given a Slope and a Point ? Find the equation of a line with slope m = 2, which passes through the point (-1, -3). Solution: Use the po
1. Write two m-files, one for the bisection method and another for Newton's method. 2. Using both the Bisection method and the Newton method answer the following: Include th
Suppose you start saving today for a $55,000 down payment that you plan to make on a house in 7 years, assume that you make no deposits into the account after the initial deposit,
Three-person Problem of Points: Pascal, Fermat and their old friend the Chevalier de Mere each put $10.00 into a pot, and agree to play a game that has rounds. Each player has the
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Euler''''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
1/cos(x-a)cos(x-b)
Solve 5x tan (8x ) =3x . Solution : Firstly, before we even begin solving we have to make one thing clear. DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like
Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest
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