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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.
volume=(1/3)(pi)(radius of base)2(height) curved surface area=(pi)(r)(l), r is radius of base and l is length of straight line connecting apex of cone with point on edge of base
Determine How many player play foot ball? In a group of athletic teams in a specific institute, 21 players are in the basket ball team, 26 players in the hockey team, 29 player
(x^2)y-(y^2)x
Find the number of square feet of pavement required for the shaded portion of the streets shown in the figure, all the streets being 50 feet wide.
verify liouville''s theorem for y''''''-y''''-y''+y=0
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
Linear Equations - Resolving and identifying linear first order differential equations. Separable Equations - Resolving and identifying separable first order differential
Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
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