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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.
I am a number yell my identity subtract 20 from me and add 30 make the total twice to reach century you still need eight
Consider a class of 55 students. The student names are placed in a hat and 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi
1. Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables
A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Φ.Prove that the height of the center of the balloon is a
Saddle Point This point in a pay off matrix is one which is the largest value in its column and the smallest value in its row. This is also termed as equilibrium point in the t
1/8 +2 3/4
Terminology of polynomial Next we need to get some terminology out of the way. Monomial polynomial A monomial is a polynomial which consists of exactly one term.
The temperature at the point (x, y) on a metal plate is given by the function f(x, y) = x 3 + 4xy + y 2 where f is in degrees Fahrenheit and x and y are in inches, with the origin
The ratio of gasoline to oil needed to run a chain-saw is 16:1. If you have 3.5 mL of oil, how many millilitres of gasoline must you add to get the proper mixture?
(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which
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