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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.
Suppose research on three major cell phones companies revealed the following transition matrix for the probability that a person with one cell phone carrier switches to another.
find a quadratic polynomial whose zeroes are 2 and -6.verify the relationship between the coefficients and zeroes of the polynomial
Determine the domain of each of the following functions. f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by
marks frequency 0-9 8 10-19 10 20-29 14 30-39 28 40-49 46 50-59 25 60-69 17 70-79 9 80-89 2 90-99 1 (
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The population of the village is 5000. If in a year, the number of males were to increase by 5% and that of a female by 3% annually, the population would grow to 5202 at the end o
Variance Square of the standard deviation is termed as variance. The semi inter-quartile range - It is a measure of dispersion which includes the use of quartile. A q
Minima, Maxima and points of inflexion a) Test for relative maximum Consider the given function of x whose graph is presented by the figure given below
find the coordinates of points of tri-section of the line joining the points (-3,0) and (6,6).
Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par
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