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Pages: [<<] 1 2 3 4 [>>] | - Page 612 - Section 9.3
Graph Theory Lessons -- Graph theory lessons, based on a software system called Petersen are available at the website of Christopher Mawata at the University of Tennessee, Chattanooga who developed this system. The software can draw, edit and manipulate simple graphs, as well as examine properties of graphs, and demonstrate them using computer animation, Among topics addressed are the handshaking theorem, isomorphism of graphs, complete graphs, subgraphs, regular graphs, platonic graphs, adjacency matrices, graph coloring, bipartite graphs, simple circuits, Euler and Hamilton circuits, trees, unions and sums of graphs, complements of graphs, line graphs, spanning trees, plane graphs, shortest paths, and minimal spanning trees. To find these lessons, go here.
http://www.utc.edu/~cpmawata/petersen/
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- Page 612 - Section 9.3
Graph Theory Lesson 7 -- A lesson on the adjacency matrix of a graph, complete with diagrams and an interactive applet can be found here.
http://www.utc.edu/~cpmawata/petersen/lesson7.htm
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- Page 616 - Section 9.3
1.3.7 Generating Graphs -- Source code for algorithms for generating graphs, including generating all graphs of a certain size and generating random graphs, can be found at the Stony Brook Algorithm Repository, run by Steven Skiena.
http://www.cs.sunysb.edu/~algorith/files/generating-graphs.shtml
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- Page 618 - Section 9.3
1.5.9 Graph Isomorphism -- Source code for algorithms for testing whether two graphs are isomorphic, including the NAUTY, can be found at the Stony Brook Algorithm Repository run by Steven Skiena. See the accompanying NAUTY link for downloading the program.
http://www.cs.sunysb.edu/~algorith/files/graph-isomorphism.shtml
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- Page 618 - Section 9.3
NAUTY -- The home page for NAUTY can be found here.
http://cs.anu.edu.au/~bdm/nauty/
(Added: Fri Jul 28 2006)
- Page 623 - Section 9.4
Paul Erdös -- A biography and photograph of Erdös can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Erdos.html
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- Page 623 - Section 9.4
Erdös Pal (1913-1996) -- Photographs and links related to Paul Erdös can be found here.
http://www.math.elte.hu/erdos/
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- Page 623 - Section 9.4
The Erdös Number Project -- Information about the Erdös number of various people is maintained by the Erdös Number Project (which has also been selected as a Geek Site of the Day) run by Jerry Grossman of Oakland University.
http://www.oakland.edu/enp/
(Added: Fri Jul 28 2006)
- Page 623 - Section 9.4
Computing Science, Graph Theory in Practice: Part I -- You can find an interesting two-part article that appeared in the Computing Science section of the American Scientist that discusses the study of large graphs, including the Web graph, call graphs, collaboration graphs, acquaintanceship graphs, and collaboration graphs, here. Check out the links in the bibliography.
http://www.americanscientist.org/template/AssetDetail/assetid/14708
(Added: Fri Jul 28 2006)
- Page 623 - Section 9.4
Computing Science, Graph Theory in Practice: Part II -- You can find an interesting two-part article that appeared in the Computing Science section of the American Scientist that discusses the study of large graphs, including the Web graph, call graphs, collaboration graphs, acquaintanceship graphs, and collaboration graphs, here. Check out the links in the bibliography.
http://www.americanscientist.org/template/AssetDetail/assetid/14717
(Added: Fri Jul 28 2006)
- Page 623 - Section 9.4
Erdös number facts -- Facts about Erdös Numbers and the collaboration graph of mathematicians can be found here.
http://www.oakland.edu/enp/
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- Page 623 - Section 9.4
The Oracle of Bacon at Virginia -- The Oracle of Bacon website at Virginia allows you to enter the name of any actor or actress and accordingly calculates the Bacon Number for that actor or actress.
http://oracleofbacon.org/
(Added: Fri Jul 28 2006)
- Page 623 - Section 9.4
Six Degrees of Kevin Bacon -- Some people claim that every actor from a movie made during the last 15 years can be connected to Kevin Bacon in six or fewer steps. You can learn more about this, and find additional links relating to this phenomenon, here.
http://www.cs.virginia.edu/cgi-bin/cgiwrap/webman/oracle/link_bacon
(Added: Fri Jul 28 2006)
- Page 625 - Section 9.4
1.4.1 Connected Components -- Source code for algorithms for finding the connected components of a graph can be found at the Stony Brook Algorithm Repository, run by Steven Skiena.
http://www.cs.sunysb.edu/~algorith/files/dfs-bfs.shtml
(Added: Fri Jul 28 2006)
- Page 625 - Section 9.4
Directed Acyclic Graphs -- Information on directed acyclic graphs (DAGs) can be found at this McGill University CS website here. Read about the diverse range of applications of DAGs.
http://www.cs.mcgill.ca/~cs251/OldCourses/1997/topic30/#BasicTerm
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- Page 625 - Section 9.4
Strong connectivity -- Information on strong connectivity and strongly connected components can be found here.
http://www1.ics.uci.edu/~eppstein/161/960220.html
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- Page 625 - Section 9.4
Tutorial on Connected Components -- You can learn about algorithms for finding the connected components of a graph at this site.
http://www.cs.cmu.edu/~scandal/applets/concomp.html
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- Page 627 - Section 9.4
Graph structure in the web -- The use of graph theory to study the Web is described in an article accessible here.
http://www9.org/w9cdrom/160/160.html
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- Page 633 - Section 9.4
Leonhard Euler Opera Omnia -- Leonard Euler's papers and books are fundamental to every branch of the mathematical sciences. More information can be found here.
http://www.springer.com/dal/home/birkhauser/historyofscience?SGWID=1-40295-69-173622221-0
(Added: Fri Jul 28 2006)
- Page 633 - Section 9.5
Graph Theory Lessons -- Graph theory lessons, based on a software system called Petersen are available at the website of Christopher Mawata at the University of Tennessee, Chattanooga who developed this system. The software can draw, edit and manipulate simple graphs, as well as examine properties of graphs, and demonstrate them using computer animation, Among topics addressed are the handshaking theorem, isomorphism of graphs, complete graphs, subgraphs, regular graphs, platonic graphs, adjacency matrices, graph coloring, bipartite graphs, simple circuits, Euler and Hamilton circuits, trees, unions and sums of graphs, complements of graphs, line graphs, spanning trees, plane graphs, shortest paths, and minimal spanning trees. To find these lessons, go here.
http://www.utc.edu/~cpmawata/petersen/
(Added: Fri Jul 28 2006)
- Page 633 - Section 9.5
1.4.7 Eulerian Cycle/Chinese Postman -- You can find source code for algorithms that find Euler circuits at the Stony Brook Algorithm Repository, run by Steven Skiena (note the terminology used at this site).
http://www.cs.sunysb.edu/~algorith/files/eulerian-cycle.shtml
(Added: Fri Jul 28 2006)
- Page 633 - Section 9.5
10.9. Euler, Leonard (1707-1783) -- A biography of Euler, and an audio file demonstrating the correct pronunciation of his name, can be found in the Historical Tidbits section of the Interactive Real Analysis. This site was prepared by Bert G. Wachsmuth at Seton Hall University.
http://web01.shu.edu/projects/reals/history/euler.html
(Added: Fri Jul 28 2006)
- Page 635 - Section 9.5
Leonhard Euler Opera Omnia -- Leonard Euler's papers and books are fundamental to every branch of the mathematical sciences. More information can be found here.
http://www.springer.com/dal/home/birkhauser/historyofscience?SGWID=1-40295-69-173622221-0
(Added: Fri Jul 28 2006)
- Page 635 - Section 9.5
10.9. Euler, Leonard (1707-1783) -- A biography of Euler, and an audio file demonstrating the correct pronunciation of his name, can be found in the Historical Tidbits section of the Interactive Real Analysis. This site was prepared by Bert G. Wachsmuth at Seton Hall University.
http://web01.shu.edu/projects/reals/history/euler.html
(Added: Fri Jul 28 2006)
- Page 635 - Section 9.5
Leonhard Euler -- A biography and a portrait of Leonhard Euler can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Euler.html
(Added: Fri Jul 28 2006)
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