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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.
Use Newton's Method to find out an approximation to the solution to cos x = x which lies in the interval [0,2]. Determine the approximation to six decimal places. Solution
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
Homework is worth 10% of my grade, quizzes are worth 30%, and tests are worth 40%. I have 15 grades in the homework section, they''re all 100''s. I have 2 grades in the quiz sectio
Q. What is Factorial? A factorial is a number with a factorial sign, !, after it. 5! is read "five factorial." 3! is read "three factorial." The factorial of a natural
find h in the parallelogram
#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c
i have a question about discret math
A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest month
if 2+2=4 what does two times two epual?
find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68
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