Weekly Log

• Week 1 (June 1st - June 7th)


• Familiarized myself with the basics of Graph Theory and Abstract Algebra
• Was introduced to recent work on the 15-puzzle and Theta-0 graph. Began preliminary research on these problems
• Read a variety of papers


• Week 2 (June 8th - June 14th)


• Continued research on this problem, exploring potential problems in optimization and feasibility of arbitrary graphs
• Gave first presentation


• Week 3 (June 15th - June 21st)


• Improved knowledge on current work in the field on this problem
• Began exploring interesting alterations to the general puzzle problem


• Week 4 (June 22nd - June 28th)


• Shifted focus toward applications of Graph pebbling, rubbling, and/or pegging
• Explored partitioning of edges within Class 0 graphs to simulate multi-color pebbling movement


• Week 5 (June 29nd - July 5th)


• Discovered family of Dual Class 0 Graph
• Formalized current lemmas and definitions
• Explored applications to complete bipartite and multipartite graphs


• Week 6 (July 6th - July 12th)


• Explored properties of graphs with diameter larger than 2, including graphs of large girth
• Refocused on the multicolor cooperation game


• Week 7 (July 13th - July 17th)


• Discovered family of complete multipartite Dual Class 0 graphs
• Isolated another interesting variant of the game
• Prepared final presentation



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