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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.
a medical clinic performs three types of medical tests that use the same machines. Tests A, B,and C take 15 minutes, 30 minutes and 1 hours respectively, with respective profits of
1/cos(x-a)cos(x-b)
Grimm plc (Grimm) has the following transactions: a) On 1 st January 2010, Grimm issued 400,000 convertible £1 6% debentures for £600,000. The professional fees associated wit
where does goes take place?
Test of homogeneity This is concerned along with the proposition that several populations are homogenous along with respect to some characteristic of interest for example; one
the radii of circular base of right circular cylinder and cone are in the ratio of 3:4 and their height are in the ratio of the 2:3 what is the ratio of their volume?
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
Kevin invested $4,000 in an account which earns 6% interest per year and $x in a different account that earns 8% interest per year. How much is invested at 8% if the total amount o
What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or
There isn't actually a whole lot to this section this is mainly here thus we can get several basic concepts and definitions out of the way. Most of the concepts and definitions in
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