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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.
classify problems in operation reseach?
1. Consider the code of size 4 (4 codewords) and of length 10 with codewords listed below. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1
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Explain Linear Equations ? Set of ordered pairs of numbers A set is an undefined term and we describe it as a "well defined" collection. We use the symbol "{ }" to denote "a se
Q. Scaling and translation for equations? Ans. If you have an equation in the form y= f(x) (if you're not familiar with functions, that just means having "y" on the left s
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find the unit rate. Round to the nearest hundredth in necessary 325 meters in 28 seconds
E1) Why do we shift the place by one, of the result in the second row of the calculation, when we multiply, say, 35 by 237 E2) Write down the algorithm for the multiplication of
There are 6 contestants for the post of chairman secretary and treasurer. These positions can be filled by any of the 6. Find the possible no. of ways whether the 3 positions may b
Cylinder The below equation is the common equation of a cylinder. x 2 /a 2 + y 2 /b 2 = 1 This is known as a cylinder whose cross section is an ellipse. If a = b we
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