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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.
Urn A contains 1 white,2 black and 3 red balls;Urn B contains 2 white,1 black and 1 red balls;and Urn C contains 4 white,5 black and 3 red balls.One urn is chosen at random and two
Adison earned $25 mowing her neighbor''s lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday. She now has $86. How much money did Adison have to
find the matrix of the linear transformations T:R2->R2 defined by T(x,y,z)=(x+2y,x-3z).
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Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?
table of 12
In the previous section we looked at the method of undetermined coefficients for getting a particular solution to p (t) y′′ + q (t) y′ + r (t) y = g (t) .....................
Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th
Draw a flowchart for accumulated principal at the end of 5 years by taking into account compound interest?
how do you find the perimeter of an equalateral triangle
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