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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.
Give a Definition of Perimeter and Area? Perimeter is the distance around a flat (2-dimensional) shape. Area is the amount of space taken up by a flat (2-dimensional) shape. is
Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.
Arc Length with Polar Coordinates Here we need to move into the applications of integrals and how we do them in terms of polar coordinates. In this part we will look at the a
Find all the eighth roots of (19 + 7 i)
As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic
write FORTRAN programme to generate prime numbers between 1 and 100
Question: The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. (a) Construct a decision tr
1+2+3+.....+n=1/2n(n+1)
Q. Illustrate Field Properties of Numbers? Ans. What the associative law of addition states is this: for any numbers a, b, and c,
Value Of The Game The game value refers to the average pay off per play of the game over an extended period of time
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