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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.
Array - when items are arranged in a regular rectangular pattern of rows and columns, counting how many there are. (e.g., if there are 3 rows of 5 girls each, how many girls are t
It takes light 5.3 × 10 -6 seconds to travel one mile. What is this time in standard notation? In order to convert this number to standard notation, multiply 5.3 through the f
Evaluate the following integral. ∫√(x 2 +4x+5) dx Solution: Remind from the Trig Substitution section that to do a trig substitution here we first required to complete t
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what is the answers of exercise 3.1
given dimensions: 130cm, 180cm, and 190cm is to be divided by a line bisecting the longest side shown from its opposite vertex. what''s the area adjacent to 180cm? ;
write 107 in expanded form.
A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and
What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or
What is Pythagorean Triples? A set of three numbers a, b, and c that can satisfy the equation A 2 +b 2 = c 2 , is called a Pythagorean triple. The following is a list of
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