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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.
Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?
what is the difference between North America''s part of the total population and Africa''s part
Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisect
Explain The Graph of an Equation and The Graph of an Inequality ? Here is the graph of the equation y = x. Notice that for every point along the line shown in the graph, the y
7 divided by 66.5
Cos(x+y)+sin(x+y)=dy/dx(solve this differential equation)
cos 8
Ask question A triangle has two sides that measure 23 ft and 30 ft. Which could be the measure of the third side? A. 5 ft B. 7 ft C. 10 ft D. 53 ft #Minimum 100 words accepted
Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp
1. The lifetime T (in days) of an electrical component has reliability function given by: R(t) = e -0.01t for time t > 0. An electrical system consists of four such components. Th
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