Difference between revisions of "(i,j)-step competition graphs"
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Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, player, companies, etc. Formally, if we let "let ''D'' be a directed graph having no multiple edges, the competition graph of ''D'' is an undirected graph G on the same node set as ''D'' and having an undirected edge ''{u<sub>i</sub>, v<sub>j</sub>}'' if and only if there exists a third node ''u''<sub>k</sub> such that ''{v<sub>i</sub>, v<sub>k</sub>}'' and ''{v<sub>j</sub>, u<sub>k</sub>}'' are directed edges in the edge set of ''D'' "[http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. | Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, player, companies, etc. Formally, if we let "let ''D'' be a directed graph having no multiple edges, the competition graph of ''D'' is an undirected graph G on the same node set as ''D'' and having an undirected edge ''{u<sub>i</sub>, v<sub>j</sub>}'' if and only if there exists a third node ''u''<sub>k</sub> such that ''{v<sub>i</sub>, v<sub>k</sub>}'' and ''{v<sub>j</sub>, u<sub>k</sub>}'' are directed edges in the edge set of ''D'' "[http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. | ||
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=='''Objectives'''== | =='''Objectives'''== | ||
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*Complete the education mdule, ''The Biology and Mathematics of Food Webs'', by '''Thursday, 6/1/17''' | *Complete the education mdule, ''The Biology and Mathematics of Food Webs'', by '''Thursday, 6/1/17''' | ||
*Attend the talk at '''11:00PM in CU 401''' | *Attend the talk at '''11:00PM in CU 401''' | ||
| − | *Enter the title, description and milestones/goals into the wiki by '''Friday, 6/2 | + | *Enter the title, description and milestones/goals into the wiki by '''Friday, 6/2''', by midnight |
*Read ''(1,2)-step competition graph of a tournament'' and have questions ready for Wednesday, 6/7/2017 | *Read ''(1,2)-step competition graph of a tournament'' and have questions ready for Wednesday, 6/7/2017 | ||
*Update Wiki at end of week or during week to reflect on what has been accomplished | *Update Wiki at end of week or during week to reflect on what has been accomplished | ||
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| + | =='''Research Logs'''== | ||
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| + | Each researcher keeps a log of the entire process, including reflections at the end of the week. These logs demonstrate the researcher's actual progress on their respective projects. Specifically, this determines whether or not they are actually reaching their milestones and completing their goals. If you would like to read them, click the researcher's name: [http://reu.mscs.mu.edu/index.php/User:Maxblack45 Max Black] or Carissa Babcock. | ||
Revision as of 03:47, 3 June 2017
Researchers: Max Black and Carissa Babcock
Mentor: Dr. Kim A.S. Factor
Background
Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, player, companies, etc. Formally, if we let "let D be a directed graph having no multiple edges, the competition graph of D is an undirected graph G on the same node set as D and having an undirected edge {ui, vj} if and only if there exists a third node uk such that {vi, vk} and {vj, uk} are directed edges in the edge set of D "(Dutton et al).
Objectives
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During this project, we will examine and explore the following:
- Previous research regarding competition graphs and (1,2)-step competition graphs of food webs
- Competition graphs and (1,2)-step competition graphs of a specific food web
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Additionally, we will further previous research by doing the following:
- Furthering research on (i,j)-step competition graphs by exploring new theory and computation
- Applying competition graphs and (i,j)-step competition graphs in new areas
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A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click here.
| Week | Description | |
| Week 1 (5/30/17-6/2/17): Orientation and Introductions |
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|---|---|---|
| Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples |
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| Week 3 (6/12/17-6/16/17): Formulating Research Questions |
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| Week 4 (6/19/17-6/23/17): Refine Research |
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| Week 5 (6/26/17-6/30/17): Mini Presentations |
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| Week 6 (7/3/17-7/7/17): Continue Individual research |
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| Week 7 (7/10/17-7/14/17): Resolve Conjectures |
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| Week 8 (7/17/17-7/21/17): Begin Finalizing Paper |
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| Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town) |
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| Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes |
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Research Logs
Each researcher keeps a log of the entire process, including reflections at the end of the week. These logs demonstrate the researcher's actual progress on their respective projects. Specifically, this determines whether or not they are actually reaching their milestones and completing their goals. If you would like to read them, click the researcher's name: Max Black or Carissa Babcock.
