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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.
Q. Define Multiplication Rule in probability? Ans. A family has two girls, Ann and Barb, and three boys, Carl, David and Earl, in it. In how many ways can the mother pick
The conjugate of the complex number a + b i is the complex number a - b i . In other terms, it is the original complex number along the sign on the imaginary part changed. Here
Find out the area of the region enclosed by y = x 2 & y =√x . Solution Firstly, just what do we mean by "area enclosed by". This means that the region we're interested in
Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let
00000000110 write in scientific notation
what is the difference between North America''s part of the total population and Africa''s part
Working Definition of Limit 1. We state that if we can create an as close to L like we want for all adequately large n. Alternatively, the value of the a n 's approach
what is the simplest form of 6:9?
A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, both head and tail have appeared , and B be the event at most one tail i
write the equation of parabola of vertex(2,-3)and focus(_1,1)
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