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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.
prove that every non-trivial ingetral solution (x,y,z)of the diophantine equation Xsquare +Ysquare=Zsquare satisfies gcd(x,y)=gcd(x,z)=gcd(y,z)
We will look at three types of progressions called Arithmetic, Geometric and Harmonic Progression. Before we start looking at the intricacies of these let us unders
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Subtraction - Vector arithmetic Computationally, subtraction is very similar. Given the vectors a → = (a 1 , a 2 , a 3 ) and b → = (b 1 , b 2 , b 3 ) the difference of the t
Steps for Alternating Series Test Suppose that we have a series ∑a n and either a n = (-1) n b n or a n = (-1) n+1 b n where b n > 0 for all n. Then if, 1.
how to use big-m method
Q. What is a Negative Number? Ans. Negative numbers are very important in mathematics. We say that positive and negative numbers are opposites of one another. Here
If 3/5=5,4/7=8,8/7=6 then, what should 9/6 be ?
Louise is estimating the cost of the groceries in her cart. She rounds the cost of every item to the nearest dollar to form her calculations. If an item costs $1.45, to what amount
Consider a discrete-time system that is characterized by the following difference equation: Y(n) = x(n)cos? 0 n, where ? 0 is constant value, x(n)are the discrete-time input
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