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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.
write a definition for associative property of multiplication in your own words and explain how you use it to compute 4*25*27 mentally
An initial species population is y(0) = 3000. At t=0 the population starts to grow exponentially with a doubling time of 2 years. Mark the only correct statement: a) The per
Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning: Assume that n 2 is
Q. What is Box-and-Whisker Plot? Ans. Line graphs or stem-and-leaf plots become difficult to manage when there is a large amount of data. Box-and-whisker plots help summa
What is 19% of 26? To ?nd out 19% of 26, multiply 26 through the decimal equivalent of 19% (0.19); 26 × 0.19 = 4.94.
a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle
Give the Introduction to Scientific Notation? In mathematics, it can be very difficult and time-consuming to do calculations involving very large and very small numbers. This i
Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d
Let R be the relation on Z + defined by aRb iff gcd(a; b) = 1 (that is, a and b have no common divisors greater than one). Explain whether R is reflexive, irreflexive, symmetri
how to prove Decidability Theorem of Logic
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