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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.
Refer the poset ({1}, {2}, {4}, {1,2}, {1,4}, {2,4}, {3,4}, {1,3,4}, {2,3,4}, ≤ ). (i) Find out the maximal elements. (ii) Find out the minimal elements. (iii) Is ther
E1) I have a three-year-old friend. He has a lot of toy cars to play with. Playing with him once, I divided the cars into two sets. One set was more spread out and had 14 cars in i
The arm of a ceiling fan measures a length of 25 in. What is the area covered through the motion of the fan blades while turned on? (π = 3.14) The ceiling fan follows a circula
Find out the Taylor Series for f (x) = e x about x = 0. Solution In fact this is one of the easier Taylor Series that we'll be asked to calculate. To find out the Taylor
What is the subset of {a,b,c}
Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures
Andre''s boss asked him to arrange bolts placing the shortest bolt near the front 1 and three fourth inch 1 and 5 eigths 1 and 11 sixteenths which is the shortest
If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value(s) of k..
G raph y = sec ( x ) Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x) Secant will not present at
The equation -2x^2-kx-2=0 has two different real soultions. find the set of possible values for k.
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