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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.
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Standard form of a complex number So, let's start out with some of the basic definitions & terminology for complex numbers. The standard form of a complex number is
Time Series and Analysis It is the statistical or mathematical analysis on past data arranged in a periodic sequence. Decision making and planning in an organization includes
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If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0
find the matrix of the linear transformations T:R2->R2 defined by T(x,y,z)=(x+2y,x-3z).
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if b+c=3a then the value of cotB/2.cotC/2 is equal to
Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).
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