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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.
Give the Examples in Real World of Proportions? Proportions can be used in cooking. For example, the following is a set of ingredients for a pasta called "Spaghetti All' Amatri
Given two functions f(x) and g(x) which are differentiable on some interval I (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int
Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is
Radius of Convergence We will be capable to illustrate that there is a number R so that the power series will converge for, |x - a| R. This number is known as the radius of
the sides of a right angle triangle are a,a+d,a+2d with a and d both positive.the ratio of a to d a)1:2 b)1:3 c)3:1 d)5:2 answer is (c) i.e. 3:1 Solution: Applying
1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.) --- Draw le
how much is 6x12
INTRODUCTION : Do you remember your school-going days, particularly your mathematics classes? What was it about those classes that made you like, or dislike, mathematics? In this
a shopkeeper buys two cameras at the same price . he sells one camera at a profit of 18% and the other at a price of 10% less than the selling price of the first camera. find his p
Mr.Tanaka has 56 students in his choir the ratio of boys to girls is 3:4 how many boys and girls are in his class
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