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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.
Extended product rule : As a last topic let's note that the product rule can be extended to more than two functions, for instance. ( f g h )′ = f ′ gh + f g ′ h+ f g h′ ( f
HOW TO ADD MIXED FRACTION
Objectives : After studying this unit, you should be able to : 1. explain the processes involved in counting; 2. explain why the ability to recite number names is no in
Before we look at simultaneous equations let us brush up some of the fundamentals. First, we define what is meant by an equation. It is a statement which indicate
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A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between two vessels is fi
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
Explain some Examples of linear in - Equation, with solution.
Prove that if f and g are functions, then f intersect g is a function by showing f intersect g = glA A={x:g(x)=f(x)}
example
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