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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.
R.2,4,6,8,10 B.8,10
x^2 + 10x +2 4
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:
/100*4500/12
WON 5 GAMES
Simplify following. Suppose that x, y, & z are positive. √ y 7 Solution In this case the exponent (7) is larger than the index (2) and thus the fir
Apply the concept of partial fraction and add the corresponding terms. The terms will get cut automatically leaving the first and last term
Q. What are Whole numbers? The set of whole numbers is the set of natural numbers with the zero thrown in: 0,1,2,3,4,... Hint: Some people remember that the whole numbers
The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable
rectangles 7cm by 4cm
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