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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.
INTRODUCTION : All of us have encountered mathematics while growing up. Some of us have grown to like it, and therefore, enjoy. doing it. Some others have developed a lukewarm rel
DECISION TREE ANALYSIS The Finance Manager of ‘Softy’ baby soap manufacturing company being successful in the first two years of the company’s operations is considering to set
Conditional probability - Rules of Probability This is the probability associated with combinations of events but given that some prior result has already been achieved with o
If I divide any number do I get the manservant 2 times
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how to find value of cos20 without using calculator
1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o
A jet flew at an average speed of 480mph from Point X to Point Y. Because of head winds, the jet averaged only 440mph on the return trip, and the return trip took 25 minutes longer
Lucas purchased his motorcycle for $5,875.98 and sold it for $7,777.77. What was his profit? To ?nd out the pro?t, you must subtract what Lucas paid for the motorcycle from the
TRIGONOMETRY : "The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth." Example:
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