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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.
If 967.234 is divided by 10, how will the decimal point move? It will move one place to the left. While dividing by multiples of 10, the decimal point is moved to the left acco
what is the difference between North America''s part of the total population and Africa''s part
How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a
A palm tree of heights 25m is broken by storm in such a way that its top touches the ground at a distance of 5m from its root,but is not separated from the tree.Find the height at
which fractions is equivalent to 5/ 6 a.20/24 b.9/10 c.8/18 d.10/15
us consider the following mass-spring-damper system: md2xdt2+cdxdt+kx=0 with m=5 kg as the mass of the body, k=1.6N/m as the spring constant and two different values of c.
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
there are 300 students in the sixth grade. if 40% of them were girls, how many boys were there?
Explain the Common Forms of Linear Equations ? An equation whose graph is a line is called a linear equation. Here are listed some special forms of linear equations. Why should
Graph y = cos (x) Solution: There actually isn't a whole lot to this one. Given the graph for -4 ? ≤ x ≤ 4 ? . Note that we can put all values of x in cosine (that wo
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