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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.
1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th
The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18cm and 15cm, respectively. Find the lengths of the sides of the triangle.
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In this case we are going to consider differential equations in the form, y ′ + p ( x ) y = q ( x ) y n Here p(x) and q(x) are continuous functions in the
Q . Mrs. Cooper asked her math class to keep track of their own grade. Michael, one of the students, lost his assignments, but he remembered the grades of 6 out of 8 assignments:
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if two lines in s plane never intersect then they are parallel
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