Dr.Gene Fiorini and Brian Nakamura

Learning the results from the graph pebbling , we try to reproduce the pebbling results in terms of rubbling ,especially for the family of trees.We try to prove the rubbling number of a complete binary tree,by finding the t-rubbling number of the subgraph of the tree. Then we try to proof the rubbling number of m-ary tree

Presentations

Meeting with my mentor, he introduced the graph pebbling and graph rubbling to me. He gave me some topics related to our research and assignment me some reading. Generally, this week I read articles and prepared for presentation.(6/5/2011)

Keeping going on reading and learning, I proofed a star of tree has a rubbling number of 4. Moving on, I tried to find the rubbling numbers of a complete binary tree. After days of trials, I found that I had troubles with the understanding and writing of a proof. Now I try to read a book called "How to Read and Do Proof."(6/12/2011)

This week has gone by so fast. The themes are still learning and proving. I tried to finish up the book "How to read and Do Proofs", but it was interrupted by the ideas coming from my mind to do the proof. Then, I did the proof of the minimum number of a complete binary tree so that the vertex/root r is reachable given any distribution of those pebbles for depth of one, two, and K (general case). I also did the same thing for M-ary trees. After that, I came up with a conjecture of rubbling number on a complete binary tree and do a proof for that at the same time. I typed up everything into worlds and sent to my mentors. I am still waiting for responds. Finially, I try to use Latex.(6/18/2011)

Looking back at this week, luckily I have made some progress. Continued from the work done last week, I generalize the maximum number of pebbles that can’t reach the root to complete M-ary tree. Based on that, I found the rubbling number of a complete 3-ary tree and generalize to the M-ary tree. Since it is difficult to draw those M-ary trees, I try to learn to draw them with asymptote. However, it is new to me so that I have to learn its programming language..(6/25/2011)

My mentor came back from his conference. We met once and tried to clear up my proof. He read my proof and gave me suggestions .(7/14/2011)

We met twice this week, but things didn't went well. I still got stuck with those proof. However, new things came into my mind. I determined to continue my research instead of writing proof. (7/14/2011)

Finally , for the new conjecture I came up last week I wrote a proof for it and my mentor said it was ok. And he helped me prood a a new conjecture with two praramenter. Today , we have our presentation. Everyone is good. Some people's presentaion are impressed. (7/14/2011)

Preparing, writing and wrapping up the report, the last week came. (7/24/2011)