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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.
What is Partially Ordered Set? Let S = {a,b,c} and A = P(S). Draw the Hasse diagram of the poset A with the partial order ⊆ (set inclusion). Ans: Let R be a relation define
ABCD is a trapezium AB parallel to DC prove square of AC - square of BCC= AB*
sketch the curve y=9-x2 stating the coordinates of the turning point and of the intersections with the axes.
((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)
(a) Derive the Marshalian demand functions and the indirect utility function for the following utility function: u(x1, x2, x3) = x1 1/6 x2 1/6 x3 1/6 x1≥ 0, x2≥0,x3≥ 0
find the series of the first twenty terms
Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.
in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are rd. what fraction of the flowers in the garden are red tulips
Find interval for which the function f(x)=xe x(1-x) is increasing or decreasing function
in 2000,nearly 18% of cars in north America were sliver. what percent of the cars sold were not sliver?
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