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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.
A particle moves along a straight line so that after t secs its distance from fixed point O on the line is given by s=(t-1)^2(t-2).find the distance from O when the velocity is zer
Find the area of shaded region of circle of radius =7cm, if ∠AOB=70 o , ∠COD=50 o and ∠EOF=60 o . (Ans:77cm 2 ) Ans: Ar( Sector AOB + Sector COD + Sector OEF) = 7
Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures
The next kind of problem seems as the population problem. Back in the first order modeling section we looked at several population problems. In such problems we noticed a single po
Cos(x+y)+sin(x+y)=dy/dx(solve this differential equation)
find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68
On 30 June 2012 Bill purchase a home by taking out a 30 year mortgage of $600,000 at 6% interest per annum, compounded months. Repayments are made at the end of each month. (a) Cal
Laura has a rectangular garden whose width is x 3 and whose length is x4. In terms of x, what is the area of her garden? Since the area of a rectangle is A = length times widt
For the given function recognize the intervals where the function is increasing and decreasing and the intervals where the function is concave up & concave down. Utilizes this info
For inequalities we contain a similar notation. Based on the complexity of the inequality the solution set might be a single number or it might be a range of numbers. If it is jus
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