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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.
what is the expiremental probability that the next toss and spin will result in 3 and tail if 1-heads,53.2-heads,49.3-heads,54.1-tail,65.2-tails,71.3-tails,62
ne nje tabak letre me permasa 100cm dhe 55cm nje nxenes duhet te ndertoje nje kuboide me permasa 20cm,25cm,40cm. a mund ta realizoje kete, ne qofte se per prerjet dhe ngjitjet humb
Suppose the economy is now ‘open’ and thus has an external demand (e.g. from the government, exports, etc.) of the dollar amounts for each respective industry. In the latest budget
RATIONAL NUMBERS All numbers of the type p/q where p and q are integer and q ≠0, are known as rational. Thus it can be noticed that every integer is a rational number
A boat tour company charges $11 for a harbour tour and averages 450 passengers on Saturdays. Over the past few months, the company has been experimenting with the price of a tour a
Differentiate following functions. h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows. h (t )
Can you show that a slope will vary along a curve (as opposed to a straight line)?
it cost $520 to plant 4 acres of corn. how much would it cost to plant 3/5 acre of corn
Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 84 feet. a) Set up an equation for the perimeter involving
Find out the area of the region bounded by y = 2 x 2 + 10 and y = 4 x + 16 . Solution In this case the intersection points (that we'll required eventually) are not going t
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