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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.
Find models of energy production and energy usage from 2 different countries, each on a different continent, which predict future energy production and demands. How was data collec
how management making future decition by using duality
47x+33y=143
1 Data is to be transmitted over Public Switched Telephone Network (PSTN) using 8 levels per signaling elements. If the bandwidth is 3000 Hz, deduce the theoretical maximum transfe
1. A machine comprises of three transformers A, B and C. Such machine may operate if at least 2 transformers are working. The probability of each transformer working is given as di
Rate of Change : The first interpretation of derivative is rate of change. It was not the primary problem which we looked at in the limit chapter, however it is the most signific
In a collection of 30 dissimilar birds, 15 eat worms, 18 eat fruit, and 12 eat seeds. Accurately 8 eat worms and seeds, 8 eat worms and fruit, 7 eat fruit and seeds, and 4 eat each
Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave the same bus station every 20 minutes. A bus to Acton and a bus to Barton both leave the bus station at 9
The Laser Computer Printer Company decides monthly what to produce during the subsequent month. They produce three types of printers, the Laser Rocket, the Alpha Laser, and the La
A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that
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