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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.
Combined mean Assume m be the combined mean Assume x 1 be the mean of first sample Assume x 2 be the mean of the second sample Assume n 1 be the size of the 1 st
Q. Samantha wrote a computer program to randomly generate two-digit numbers between 00 and 99. Let X be the random 2 digit number generated by the computer. Find the distributio
One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer? Let x = the greater integer and y = the lesser int
Before independence, Bangladesh was called Ceylon East Pakistan Bhutan Bangalore Which of the following countries does not have a monarch as head of state? Canada Australia Eire
what is 5x - 14x + 7x =
Mathematical Statements Are Unambiguous : Consider any mathematical concept that you're familiar with, say, a sphere. The definition of a sphere is clear and precise. Given any o
The null hypothesis It is the hypothesis being tested, the belief of a specific characteristic for illustration, US Bureau of Standards may walk to a sugar making company along
Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po
y=f(a^x) and f(sinx)=lnx find dy/dx? Solution) dy/dx exist only when 0 1 as the function y = f(a^x) itself does not exist.
What is equivalence relation? Prove that relation 'congruence modulo' ( ≡mod m) is an equivalence relation. Ans: A relation R illustrated on a nonempty set A is said to be
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