Graph Theory Lessons

Author : Dr. Christopher P. Mawata, Department of Mathematics, University of Tennessee at Chattanooga
Publication Date : June 2004

About the Lessons:

These are the entire 23 lessons of Graph Theory taught in Department of Mathematics University of Tennessee at Chattanooga. It utilizes a java software, Petersen, written by Christopher P. Mawata which can draw, edit and manipulate simple graphs, examine properties of the graphs, and demonstrate them using computer animation. The software can display information about a graph like the number of vertices and their degrees, the adjacency matrix, the number of components, and articulation points. It can find complements of graphs, line graphs, find the chromatic number of a graph, check if a graph is bipartite, check if two graphs are isomorphic or if one graph is a subgraph of another and find the dual graph of a planar graph in many cases. Petersen also demonstrates Euler and Hamilton circuits, searches, and algorithms for finding minimum spanning trees.

The subject matter addressed in these lessons are 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. These topics are central to graph theory and essential to further learning in the area.

Intended Audience and Hardware requirements:

These lessons are targeted at undergraduate beginning classes in Graph Theory. The students who use the software at UTC, the University of Tennessee at Chattanooga, are mathematics majors for whom it is an elective course and computer science students for whom it is a required course. It is assumed that the students using the software and lessons have some measure of mathematical sophistication; for instance that they are able to write an induction proof etc. They have done second semester calculus and a course in computer programming. The prerequisite courses give an indication of the level of mathematical maturity assumed. The Petersen software will run under Windows 3.1, Windows 95 or better.

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