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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 ladder sets against a wall at an angle α to the horizontal. If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall ma
write a program C++ programming language to calculate simple interest, with it algorithm and it flowchart
1. A point P(a,b) becomes (3,c) after reflection in x - axis, and (d,6) after reflection in the origin. Show that a = 3, b = - 6, c = 6, d = 2 2. If the pair of lines ax² + 2pxy
Explain Combining Negative Signs in integers? You've learned about positive and negative integers. BASICS : When you place a negative sign in front of an integer, you get
evaluate sin 15
formula for non negative solutions integral
1. Let R and S be relations on a set A. For each statement, conclude whether it is true or false. In each case, provide a proof or a counterexample, whichever applies. (a) If R
Suppose a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is provided, the area between S and the x-axis plus the covered area between S and
Find all the real solutions to cubic equation x^3 + 4x^2 - 10 =0. Use the cubic equation x^3 + 4x^2 - 10 =0 and perform the following call to the bisection method [0, 1, 30] Use
A card is drawn from a well shuffled deck of cards (i) What are the odds in favour of getting spade? (Ans: 1:3, 3:1, 3:10, 1:25) (ii) What are the odds against getting a spa
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