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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.
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
if a,b,c are in HP
Solve for x: 4 log x = log (15 x 2 + 16) Solution: x 4 - 15 x 2 - 16 = 0 (x 2 + 1)(x 2 - 16) = 0 x = ± 4 But log x is
Given f ( x ) = 3x - 2 determine f -1 ( x ) . Solution Now, already we know what the inverse to this function is as already we've done some work with it. Though, it
Find out all the critical points for the function. Solution To determine the derivative it's probably simple to do a little simplification previous to we in fact diffe
how to select out time for m2
Classify the following discrete-time signals as energy or power signals. If the signal is of energy type, find its energy. Otherwise, find the average power of the signal. X 1
Describe Subtracting Negative Fractions? Subtracting two fractions, whether one is positive and one is negative, or whether they are both negative, is almost the same process a
Brent covered 3 1/5 by a number and got 4 1/2 what number dis he divide by? The answer is either 1 9/16, or 32/45. Which one is the answer, and how did you get it?
Example Find the Highest Common Factor of 54, 72 and 150. First we consider 54 and 72. The HCF for these two quantities is calculated as follows:
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