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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.
The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.
Natureland garden center buys lawn mowers that list for $679.95 less a 30% discount. What is the dollar amount of the discount?
Determine or find out if the subsequent series is convergent or divergent. If it converges find out its value. Solution To find out if the series is convergent we fir
find the sum of the following series upto n terms: 1*2+2*4+3*8+4*16+.....
How to Simplifying Square Roots ? To simplify square roots, 1. Factor the radicand into primes. 2. Circle each pair of like numbers. 3. For each pair of like numbers, place
Devise one activity each to help the child understand 'as many as' and 'one-to-one correspondence'. Try them out on a child/children in your neighbourhood, and record your observat
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Company A and Company B have spent a lot of money on research to develop a cure for the common cold. Winter is approaching and there is certainly going to be a lot of demand for th
Now we take up combinations and its related concepts. Combinations are defined as each of the groups or selections which can be made by taking some or all of the
Two people are 50 feet separately. One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what
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