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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.
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual
By using the above data compute the quartile coefficient of skewness Quartile coefficient of skewness = (Q3 + Q1 - 2Q2)/(Q3 + Q1) The positio
To begin with we have counting numbers. These numbers are also known as natural numbers and are denoted by a symbol 'N'. These numbers are obtai
y+7 3y-2 --- = 1 + ---- 3 5
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
Determine the equation of the tangent line to r = 3 + 8 sinθ at θ = Π/6. Solution We'll first need the subsequent derivative. dr/dθ = 8 cosθ The formula for the deriv
the operations of cyclic permutations
Explain Basic Geometric Concepts ? Points, lines, and planes are the most fundamental concepts in the study of geometry. Points A point has no length, width or heig
(-85) from (-21) and explain me
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