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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.
Determine the equation of the tangent line to r = 3 + 8 sinθ at θ = Π/6. Solution We'll first need the subsequent derivative. dr/dθ = 8 cosθ The formula for the deriv
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what is the difference between North America''s part of the total population and Africa''s part
Determine if the acceleration of an object is given by a → = i → + 2 j → + 6tk → find out the object's velocity and position functions here given that the initial velocity is v
Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi
use the expansion of (1-x)^7 to find the value of 1.998^7 correct to five significant figures
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Find and classify the equilibrium solutions of the subsequent differential equation. y' = y 2 - y - 6 Solution The equilibrium solutions are to such differential equati
Eduardo is merging two 6-inch pieces of wood with a piece in which measures 4 inches. How many total inches of wood does he have? This problem translates to the expression 6 ×
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