Reference no: EM132385776

Math 381 Writing Assignment - Executable Code & report

Please make sure to follow and include all components.

Let x=9.

Define a graph G = (V,E) as follows.

Let V = {1, 2, 3, . . . , 10}.

Define E = {(i, j): i, j ∈ V, i ≠ j, cos((i + j)(1 + x)) > 0}.

Create and solve (using lpsolve) an IP to find the chromatic number of G, χ(G).

Write a piece of code to generate the lpsolve input file.

Be sure to give a complete explanation of your method of solution.

Explicitly list your objective function and all constraints in your IP.

Include all code you write to solve the problem, and all software output.

You are welcome to use any programming language(s).

Please include the following components in this format:

1. Problem statement

2. Description of solution method including the mathematical formulation of the IP you will be using. Explain your method thoroughly.

3. Code to generate the lpsolve input file

4. The lpsolve input file. Be sure to truncate it: give one or two examples of each type of constraint, then remove the others, and indicate the number of constraints of each type removed.

5. Information about how you ran lpsolve on the above file, including run time and machine used, and the lpsolve solution output. Be sure to truncate it: leave out all variables which are equal to zero, and indicate that you have done this (e.g., "All other variables equal zero.").

6. Answer the question.

7. Include a figure that illustrates the feasibility of coloring your graph with the minimum number of colors you are claiming. Spend some time finding an arrangement of the vertices in the plane that makes the figure a little more readable (e.g., arranging the vertices in order around a circle will probably not result the best figure).

Attachment:- Assignment File - Executable Code & report.rar