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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.
Find the ratio in which the line segment joining A(6,5) and B(4,-3) is divided by the line y=2 (Ans:3:5) Ans : Let the ratio be k:1 x = 4 k + 6/ k +1 y
Trace the curve y 2 = (x + 2) 2 (x - 6). Clearly state all the properties you have used for tracing it(e.g., symmetry about the axes, symmetry about the origin, points of interse
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The subsequent topic that we require to take a look at is the determinant of a matrix. The determinant is in fact a function that gets a square matrix and converts this in a number
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la expresión que permite calcular el radio medio de la órbita de cada planeta es?
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