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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.
seven more than a number is less than or equal to -18
Give me an example , please : 1 over 2 , 14 over twenty-eight
Set M= {m''s/m is a number from 5 to 10}
Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans: Given : - ∠APB = 120o Construction : -Join OP To prove : -
i want to get market value of 10 popular shares of all working days in a week
Nancy, Jennifer, Alex, and Joy ran a race. Nancy's time was 50.24 seconds, Jennifer's was 50.32, Alex's was 50.9, and Joy's was 50.2. Whose time was the fastest? The fastest ti
1. Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which x e =
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
Implicit Differentiation : To this instance we've done quite a few derivatives, however they have all been derivatives of function of the form y = f ( x ) . Unluckily not all
Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc
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