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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.
Given a standard 2x3 matrix show the ideal formed by the 2x2 minors is Prime.
Example of Probability: Example: By using a die, what is the probability of rolling two 3s in a row? Solution: From the previous example, there is a 1/6 chance of
find a quadratic equation whose roots are q+1/2 and 2p-1 with p+q=1
If f(x) is an infinitely differentiable function so the Taylor Series of f(x) about x=x 0 is, Recall that, f (0) (x) = f(x) f (n) (x) = nth derivative of f(x)
How do you simplify 10:30:45
what is trecnametry
Find out if the following series is convergent or divergent. Solution There really is not very much to these problems another than calculating the limit and then usin
There are really three various methods for doing such integral. Method 1: This method uses a trig formula as, ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c
The Geometric Index or Industrial Share index The Geometric Index or Industrial Share index is an index of 30 selected top industrial companies. This is calculated by taking a
graphing
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