Web Links for Chapter 8
Page 377, Graph Theory
Extensive lessons on graph theory by Christopher Mawata, University of Tennessee at Chattanooga, are available at http://www.utc.edu/~cpmawata/petersen/. Another introductory site is http://www.c3.lanl.gov/mega-math/workbk/graph/grbkgd.html. My program graph_ge.c generates random graphs of various types.
Page 380, Bacon Numbers
The Oracle of Bacon at http://OracleOfBacon.org gives an upper bound (which is usually exact) on the Bacon number of almost any actor. The site can also give an upper bound on the length of a shortest path from almost any actor to any other.
Page 382, The n-Cube (Hypercube)
See http://en.wikipedia.org/wiki/Hypercube.
Page 386, Paul Erdos
A biography of Erdos is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Erdos.html. The Erdos Number Project at http://www.oakland.edu/enp/ is maintained by Jerrold Grossman, Oakland University.
Page 391,
A discussion of the Koenigsberg Bridge Problem is at http://mathforum.org/isaac/problems/bridges1.html. A biography of Euler is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html.
Page 400, Hamiltonian Cycles and the Traveling Salesperson Problem
A biography of Hamilton is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html. The Hamiltonian Page with vast references about the Hamiltonian cycle problem is at http://www.ing.unlp.edu.ar/cetad/mos/Hamilton.html. Source code for solving the Hamiltonian cycle problem is at http://www.cs.sunysb.edu/~algorith/files/hamiltonian-cycle.shtml. My own source code is hamilton.c. Information about the traveling salesperson problem is at http://www.pcug.org.au/~dakin/tsp.htm and http://www.ing.unlp.edu.ar/cetad/mos/TSPBIB_home.html.
Page 402, Gray Codes
See http://en.wikipedia.org/wiki/Gray_code for information about the inventor, Frank Gray, as well as applications and history of Gray codes. For more history and links see http://www.nist.gov/dads/HTML/graycode.html.
Page 404, The Knight’s Tour
See http://www.tri.org.au/knightframe.html. http://www.velucchi.it/mathchess/knight.htm contains many links to pages about the knight's tour. http://www.behnel.de/knight.html is concerned with the knight's tour and backtracking.
Page 408, Dijkstra’s Shortest-Path Algorithm
An Animation of Dijkstra’s shortest-path algorithm can be found at http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/index.html. Source code is http://www.cs.sunysb.edu/~algorith/files/shortest-path.shtml.
Page 413, Adjacency Matrix
See http://mathworld.wolfram.com/AdjacencyMatrix.html.
Page 415, Incidence Matrix
See http://mathworld.wolfram.com/IncidenceMatrix.html.
Page 425, Planar Graphs
An algorithm for determining whether a graph is planar is at http://www.cs.sunysb.edu/~algorith/files/planar-drawing.shtml.
Page 426, Kuratowski
A biography of Kuratowski is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kuratowski.html.
Page 431, Instant Insanity