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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.
use only the digits 1,2,3 and 4 in any order to write an expression for the numbers 1 to 100. you may only use each digit once. You may use exponents of 1,2,3 and 4 in some of th
1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side
I gave my niece a whole heap of beads and showed her how to divide it up into sets of 10 beads each. Then I showed her how she could lay out each set of I0 beads in a line, and cal
5 hockey pucks and three hockey sticks cost $23. 5 hockey pucks and 1 hockey stick cost $20. How much does 1 hockey puck cost?
In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may
Consider the function f(x) = x 2 - 2x - 1. (a) Factorise f(x) exactly. (b) Find the exact points (x and y coordinates required) where the graph of y = f(x) cuts the x and y-
A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systol
please suggest me that how can i get the term papers topics?
5+5
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