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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.
Definition of Natural exponential function: The natural exponential function is f( x ) = e x where, e= 2.71828182845905........ . Hence, since e > 1 we also know that e x
the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
Multiple response question.Zack puts a mug of water ni his microwave oven. He knows that the final temperature of the water will be a function of the number of seconds he heats the
Q. What are Mutually Exclusive events? Mutually Exclusive Events are mutually exclusive if they cannot occur at the same time. For example, if you roll one die, you canno
which quadrilaterals have only 1 pair of parallel sides
Substitution Rule Mostly integrals are fairly simple and most of the substitutions are quite simple. The problems arise in correctly getting the integral set up for the substi
What is a five number summary?
Three payments of $2000 (originally due six months ago, today, and six months from now) have been renegotiated to two payments: $3000 one month from now and a second payment due in
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A rectangular garden has a width of 20 feet and a length of 24 feet. If each side of the garden is increased through the similar amount, how many feet is the new length if the new
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