Graph and Trees

1. 7 Bridges of Königsberg

2. Tymoczko, Thomas (1979), "The Four-Color Problem and Its Philosophical Significance", Journal of Philosophy 76(2) (February): 57-83.
   Also see:
   • Gardner, Martin (1966), Martin Gardner's New Mathematical Diversions from Scientific American (New York: Simon & Schuster), Ch. 10: "The Four-Color Map Theorem", pp. 113-123, 250-251.

3. Dipert, Randall R. (1997), "The Mathematical Structure of the World: The World as Graph", Journal of Philosophy 94(7) (July): 329-358.
   • "[T]he concrete world is a single, large structure induced by a single, two-place, symmetric relation, and thus best analyzed as a certain sort of graph."

4. Hayes, Brian (2008), "Accidental Algorithms", American Scientist 96(1) (January-February): 9-13.
   • This article should be available to the general public. If it is not, please let me know, and I will make a copy available.

   • Discusses Eulerian and Hamiltonian circuits, and cites the work of former UB CS faculty member Jin-Yi Cai.

5. Tree examples (Fig. 10.1.2 from text)

6. The Tree of Porphyry
   • from John F. Sowa, Knowledge Representation (Pacific Grove, CA: Brooks/Cole).
   • English translation of Peter of Spain's (Pope John XXI's) version, also from Sowa.

7. "One way to understand the Web...is as a graph whose nodes are Web pages (defined as static HTML documents) and whose edges are the hypertext links among these nodes."
   • From: Hendler, James; Shadbolt, Nigel; Hall, Wendy; Berners-Lee, Tim; & Weitzner, Daniel (2008), "Web Science: An Interdisciplinary Approach to Understanding the Web", Communications of the ACM 51(7) (July): 60-69; quote on p.64.

8. Special Issue on AI and Networks, AI Magazine 29(3) (Fall 2008).
   • Contains articles on applications of graph theory to artificial intelligence and the World Wide Web. In particular, the introductory article has a nice summary of elementary graph theory:
     • desJardins, Marie; Gaston, Matthew E.; & Radev, Dragomir (2008), "Introduction to the Special Issue on AI and Networks", AI Magazine 29(3) (Fall): 11-15.