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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.
List some activities/tasks/exercises that you would give a class of 50 children to do to make them aware about patterns, and to articulate what the patterns are. You must be won
Importance of positioning
The function A(t) = 5(0.7)^t was used to define the amount A in milliliters of a drug in the bloodstream t hours after the drug was ingested. Determine algebraically the time it wi
Graph ( x + 1) 2 /9 -( y - 2) 2 /4 =1 Solution It is a hyperbola. There are in fact two standard forms for a hyperbola. Following are the basics for each form. H
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Explain Combining Negative Signs in integers? You've learned about positive and negative integers. BASICS : When you place a negative sign in front of an integer, you get
Now come to addition and subtraction of rational expressions. Following are the general formulas. (a/c) + (b/c) = (a + b)/c
what is the business application of matrices
1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.) --- Draw le
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