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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 the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
What lines are invariant under the transformation [(103)(01-4)(001)]? I do not know where to even begin to solve this. Please help!!
In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti
Solving for X in isosceles triangles
If the mass is 152.2g and the volume is 18cm3, then what is the density?
in one point of the circle only one tangent can be drawn. prove
Fermat Catalan Conjecture
The Shape of a Graph, Part I : In the earlier section we saw how to employ the derivative to finds out the absolute minimum & maximum values of a function. Though, there is many
Indeterminate forms Limits we specified methods for dealing with the following limits. In the first limit if we plugged in x = 4 we would get 0/0 & in the second limit
Change of base: The final topic that we have to look at in this section is the change of base formula for logarithms. The change of base formula is,
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