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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.
Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation: y''''-xy''-y=0
Tchebyshev Distance (Maximum Travel Distance per Trip Using Rectilinear Distance): It can be calculated by using following formula: d(X, Pi) = max{|x - ai|, |y - bi|} (Source
Get the Delta H (Enthalpy) and Delta V (Volume) of the both components below and compare by ratio. You need to use clapeyron equation and also need to draw the graphs. S A LG
circumference of a circle
writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
Root Test- Sequences and Series This is the final test for series convergence that we're going to be searching for at. Like with the Ratio Test this test will as well tell wh
Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let
The next kind of problem seems as the population problem. Back in the first order modeling section we looked at several population problems. In such problems we noticed a single po
Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave the same bus station every 20 minutes. A bus to Acton and a bus to Barton both leave the bus station at 9
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