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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.
A framed print measures 36 by 22 in. If the print is enclosed by a 2-inch matting, Evaluate the length of the diagonal of the print? Round to the nearest tenth. See Example.
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Objectives After studying this unit, you should be able to explain how mathematics is useful in our daily lives; explain the way mathematical concepts grow; iden
Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3
evaluate the expression a) 10C4 b) 10P4.....I do not understand this
A patient will receive hemodialysis for 2.5 hours. The amount of fluid removed per hour is 1.4 liters. The total amount removed in liters, will be
A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time. And if the train were
Now we need to discuss graphing an equation. The first question which we have to ask is what accurately is a graph of an equation? A graph is the set of all the ordered pairs whos
Five cards - the ten, jack, queen, king and ace, are well shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is
One of the well-known class of models that involve a simple difference equation are models of mean reversion. These models typically take the form yt+1 - yt = -a(yt - μ)where 0
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