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Question: (a) Prove that two graphs which are isomorphic must contain the same number of triangles.
(b) Prove that, for any n ≥ 4, two isomorphic graphs must contain the same number of n-cycles.
(c) How many edges are there in the graphs G1 and G2? How many vertices? What is the degree sequence of each graph? Are the graphs isomorphic? Explain.
Find the level of production that will maximize revenue. If the producer s costs are given by C(x) = 2 + 3x what should his level of production be to maximize profits?
They are considering 5 different sofas , 2 different chairs, and 6 different tables. They plan to select one item from each category. Determine the number of different ways they can select the furniture.
Use the iterative method for solving the Leontief input output model for the following systems of equations. You only need to go to the sixth iterate,
what is the lenght and width of a rectangle if the length is 100 feet more than the width and the perimiter is 1320 feet?
Repeat (a) if the friends consist of three single people and three married couples and, if a husband or wife is invited, the spouse must be invited too.
Math 104: Final exam. Given a function f on [a, b], define the total variation of f to be, Vf = sup{k=1∑n|f(tk)-f(tk-1)|}. where the supremum is taken over all partitions P = {a = t0
An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 250 miles per hour. What is the speed of the airplane?
Solve this model by using graphical analysis
case study applications paper choose one of the following case studiesbull food websbull coding theorybull network
The perimeter of the rudder of a boat can be described as the region bound by y = -0.5x2v(4 - x2), and the x-axis.
A trust fund is being set up with a single payment of K. This amount is to be invested at a fixed annual interest rate of r.
F is the linear transformation that orthogonally projects each vector inR3onto the plane defined byx+2y+2z=0 a) Enter an orthonormal basis for the subspace defined by the plane. Your answer should be a list of vectors, e.g. (1,2,3),(4,5,6)?
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