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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.
Universal set The term refers to the set which contains all the elements such an analyst wishes to study. The notation U or ξ is usually used to denote universal sets.
Find the values of x and y
larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?
Marks obtained by 70 students are given below: M arks 20 70 50 60 75 90 40 No.
A certain bank pays 3.4% interest per year for a certificate of deposit, or CD. What is the total balance of an account after 18 months along with an initial deposit of $1,250?
From past experience a machine is termed to be set up correctly on 90 percent of occasions. If the machine is set up correctly then 95 percent of good parts are expected however i
Will has a bag of gumdrops. If he eats 2 of his gumdrops, he will have among 2 and 6 of them left. Which of the subsequent represents how many gumdrops, x, were originally in his b
get the viscosity of particle to apply the stoke''s law
Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. While any three of these members are selected to be a team, the league aims to use the sum of
Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the
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