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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.
I need help with this question: Find the probability that two quarters and a nickel are chosen without replacement from a bag of 8 quarters and 12 nickles.
#question what is input and output analysis
Write 3.5 × 104 in decimal notation? Move the decimal point 4 places to the right to get 35,000.
Which expression below is equal to 5? The correct order of operations must be used here. PEMDAS tells you in which you should do the operations in the subsequent order: Pare
a muffin recipe calls for three forth of a cup of sugar and one eight of a cup of butter. travis accidentally put in one whole cup of butter. how much sugar does travis need to put
1) let R be the triangle with vertices (0,0), (pi, pi) and (pi, -pi). using the change of variables formula u = x-y and v = x+y , compute the double integral (cos(x-y)sin(x+y) dA a
Find the derivatives of the following functions a) y = 5x 4 +3x -1-x 3 b) y = (x+1) -1/2 c) y= e x2+1 d) y= e 3x lnx e) y =ln(x+1/x)y
Vectors This is a quite short section. We will be taking a concise look at vectors and a few of their properties. We will require some of this material in the other section a
Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).
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