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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.
Anne, Betty and Carol went to their local produce store to buy some fruit. Anne bought one pound of apples and two pounds of bananas and paid $2.11. Betty bought two pounds of appl
Q. Define Degrees and Radians? Ans. Just as your height can be measured in meters or feet and your weight can be measured in pounds or kilograms, angles can be measured in
Find out the length of y = ln(sec x ) between 0 x π/4. Solution In this example we'll need to use the first ds as the function is in the form y = f (x). So, let us g
Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia
A jar contains 54 marbles each of which is blue , green or white. The probability of selecting a blue marble at random from the jar is 1/3 and the probability of selecting a green
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A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. The solid is placed in a cylindr
properties
calculates the value of the following limit. Solution Now, notice that if we plug in θ =0 which we will get division by zero & so the function doesn't present at this
A lotus is 2m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original positio
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