Question

The Good Will Hunting Problem Due Sunday, September 15, 2019 by 11:59 p.m. (Submit on Webcourses and a hard copy in class in next class after subemission) ) In the Movie, Good Will Hunting, the main character, Will Hunting, played by Matt Damon, is a janitor at a university. As he is mopping floors, he notices a problem posted on a board as a challenge to math students. The solution to the problem uses network analysis. Given the graph G 2 a) Find the adjacency matrix A of the ghgh G. b) Find the matrix giving the number of three-step.aalks for the gpa G c) Give a list of all 3-steps walks from node 1 to node 2 2) In the second problem (in the movie), Professor Gerald Lambeau come to the class and announces a problem that has taken MIIT professors 2 years to solve. He boldly proclaims that the so-called gauntlet has been thrown down. Only strong students would dare try and solve it. The problem is Find all homeomorphically irreducible trees of degree ten (ic. 10 vertices). In the language of network science, the problem is to find of fully connected networks with 10 nodes and containing no cycles. Essentially, we need to join ten nodes together such that a) All nodes are connected to at least one other node. b) No cycles are allowed and only one link is allowed between any two nodes. c) Most importantly, no node can have degree of 2. d) How many can you create? Show all the nodes 3) Now try to do the same thing you did in question (2) but this time for 7 and 8 nodes Hint: Watch the Movie and have fan..

i took a better photo.

Answer 1

1 a) The following is the required adjacency matrix A

1	1	0	1
1	0	2	1
0	2	0	0
1	1	0	0

b) Cubing the matrix A would give the number of three-step walks in G.

7	9	4	5
9	3	12	8
4	12	0	2
5	8	2	3

c)

The list of all 3-step walks from 1 to 2 are:

• a-b-d
• a-a-c
• c-e-e
• c-e-f
• c-f-e
• c-f-f
• c-c-c
• c-d-d
• b-b-c