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4434Graph Theory Lessons
https://www.merlot.org/merlot/viewMaterial.htm?id=84776
The applets contain topics typically found in undergraduate graph theory and discrete structures classes like null graphs, the handshaking lemma, isomorphism, 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, minimal spanning trees. The applet utilizes Petersen software written by the author. Peterson can draw, edit and manipulate simple graphs, examine properties of the graphs, and demonstrate them using computer animation.Sat, 24 Sep 2005 00:00:00 -0700Discrete Math Resources
https://www.merlot.org/merlot/viewMaterial.htm?id=363275
This site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley and Winston Crawley. Requires Adobe Flash player.Tue, 27 Jan 2009 19:07:46 -0800Graph Theory: Trees
https://www.merlot.org/merlot/viewMaterial.htm?id=86622
This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is Trees. The user will explore full binary, ternary and n-ary trees, the relationship of parent and child, and depth-first and breadth-first traversal.Sat, 6 May 2006 00:00:00 -0700Euler Circuits, Hamilton Circuits, Directed Graphs
https://www.merlot.org/merlot/viewMaterial.htm?id=86621
This applet is a component of a larger site on Graph Theory. It introduces Euler Circuits and Hamilton Circuits and provides opportunities to investigate their properties using Peterson software.Sat, 6 May 2006 00:00:00 -0700Graph Theory: Spanning Trees
https://www.merlot.org/merlot/viewMaterial.htm?id=86623
This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is on Spanning Trees. The user will explore depth first and breadth first methods of developing spanning trees from a connected graph.Sat, 6 May 2006 00:00:00 -0700Graph Matching Algorithms
https://www.merlot.org/merlot/viewMaterial.htm?id=974114
This video was recorded at Machine Learning Summer School (MLSS), Canberra 2005. Graph matching plays a key role in many areas of computing from computer vision to networks where there is a need to determine correspondences between the components (vertices and edges) of two attributed structures. In recent years three new approaches to graph matching have emerged as replacements to more traditional heuristic methods. These new methods are: * Least squares - where the optimal correspondence in determined in terms of deriving the best fitting permutation matrix between sets. * Spectral methods - where optimal correspondences are derived via subspace projections in the graph eigenspaces. * Graphical models - where algorithms such as the junction tree algorithm are used to infer the optimal labeling of the nodes of one graph in terms of the other and that satisfy similarity constraints between vertices and edges. In this lecture we review and compare these methods and demonstrate examples where this applies to point set and line matching.Tue, 10 Feb 2015 13:28:34 -0800Graph Theory Tutorials
https://www.merlot.org/merlot/viewMaterial.htm?id=86754
This is a series of short interactive tutorials introducing the basic concepts of graph theory. There is not a great deal of theory here, but enough will be taught to wet your appetite for more!Fri, 2 Jun 2006 00:00:00 -0700Integer Optimization and the Network Models
https://www.merlot.org/merlot/viewMaterial.htm?id=80563
It covers integer and network optimization with numerical examples and applicationsSun, 15 Feb 2004 00:00:00 -0800'Lies, Damn Lies, and Statistics': A Critical Assessment of Preferential Attachment-type Network Models of the Internet
https://www.merlot.org/merlot/viewMaterial.htm?id=940895
This video was recorded at 4th European Conference on Complex Systems. Basic Question: Do the available Internet-related connectivity measurements and their analysis support the sort of claims that can be found in the existing complex networks literature? Key Issues: What about data hygiene? What about statistical rigor? What about model validation? Author discusses some of the main problems and challenges associated with measuring, inferring, and modeling various types of Internet-related connectivity structures. To this end, he uses some known examples to illustrate the need to understand the process by which Internet connectivity measurements are obtained, explore the sensitivity of inferred graph properties to known ambiguities in the data, be more critical with respect to the dominant, preferential attachmenttype network modeling paradigm, and be more serious/ambitious when it comes to model validation. Ignoring any of these issues is bound to produce results that are best described by the well-known aphorism "lies, damned lies, and statistics."Sun, 8 Feb 2015 21:11:25 -0800A Century of Graph Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=944078
This video was recorded at Predavanja, seminarji in srečanja na Fakulteti za matematiko in fiziko. Graph theory has changed completely from the late-19th century to the late 20th century, from a collection of mainly recreational problems to a well-developed mainstream area of mathematics. In this talk I outline its development over this period, both chronologically and thematically.Sun, 8 Feb 2015 21:38:06 -0800