Hello guys, sorry for the late reply. I have been a little bit busy.
Section 8.1 is just an introduction to what graphs are, which in our case should be more of a recap. As expected, the book did explain basic terms such as vertices, edges, degree of vertex, indegree, outdegree,and connected and disconnected graphs. I do not think there is a need to define any of them here, but if anyone wants me to, just make a comment, and I will be sure to reply. The book also included very popular problems involving graphs such as the bridge problem, the Hamiltonian cycle problem, and others similar to them. I am guessing most of us have heard and practiced these problems at least once in our lives.
Section 8.2 gave a nice description on how Seymour Benzer used graphs and graph theory, along with his experiment on bacteria to show that genes are linear.
Ore,
I agree that most of 8.1 is standard graph theory and if anyone found something in that section confusing, then looking things up on wikipedia should clear most questions up. For example, they define a tree as a “simply connected graph with no cycles”. I found the word “simply” confusing as “simply connected” is a math phrase which has a precisely meaning in topology. If you go look at the definitions on wikipedia, you can either define a tree as “a simply connected graph” (in the topological sense), or as a “connected graph with no cycles”. These two definitions are equivalent. Mixing the two is unnecessary and a little confusing, I thought.
I did think it was interesting that a problem which seems super hard at first (the chess problems), turns out to be trivial once you encode it as a graph theory question. The main point is to recognize that graph theory is useful whenever you have a problem about points (in this case, squares of the chessboard) and connections between the points (in this case, they’re connected if you can get from one to another with a move by the knight).
The only thing about 8.2 I thought I should mention is that in Benzer’s experiment (at least if I understood it correctly), he didn’t actually prove that the DNA was linear. What he found was that his data was consistent with DNA being linear, but it could have been that his data all happened to be measuring on a section of DNA which happened to be linear (for example, in figure 8.12b, you could have done all your sampling on the left half of the Y shaped picture, and not seen the branch on the right half).
If there was a branch and he sampled at that point like in figure 8.12b, then his method would have detected it. So his method provides evidence that the DNA is linear, but doesn’t _prove_ it, strictly speaking. Of course, I assume he ran this experiment many times and so it is highly unlikely that he always got graphs showing linear DNA just by luck.
By: jonkujawa on August 10, 2011
at 3:15 pm
I completely agree with you on section 8.2. If his experiment was on a different section, he could have gotten another result. The problem is that the book itself did not give detailed information on what exactly he did with his experiment, which is why I did not talk about it at all.
By: oreadex on August 11, 2011
at 12:30 am