Graph Theory

SUBJECT > Discrete Mathematics : Graph Theory : General Graph Theory

The mathematical study of the properties of the formal mathematical structures called Graphs.

Adjacency Matrix, Adjacency Relation, Articulation Vertex, Blue-Empty Coloring, Bridge (Graph), Chromatic Number, Chromatic Polynomial, Circuit Rank, Crossing Number (Graph), Cycle (Graph), Cyclomatic Number, Degree, Dijkstra's Algorithm, Eccentricity, Edge-Coloring, Edge Connectivity, Eulerian Circuit, Eulerian Trail, Factor (Graph), Floyd's Algorithm, Girth, Graph Diameter, Graph Radius, Graph Two-Coloring, Group Theory, Hamiltonian Circuit, Hasse Diagram, Hub, Indegree, Integral Drawing, Isthmus, Join (Graph), Local Degree, Monochromatic Forced Triangle, Outdegree, Party Problem, Pólya Enumeration Theorem, Pólya Polynomial,Ramsey Number, Re-Entrant Circuit, Separating Edge, Tait Coloring, Tait Cycle, Traveling Salesman Problem, Tree, Tutte's Theorem, Unicursal Circuit, Valency, Vertex Coloring, Walk

References

Graph Theory

Beinecke, L. W. and Wilson, R. J. (Eds.). Graph Connections: Relationships Between Graph Theory and Other Areas of Mathematics. Oxford, England: Oxford University Press, 1997.

Berge, C. The Theory of Graphs. New York: Wiley, 1962.

Bogomolny, A. ``Graphs.'' http://www.cut-the-knot.com/do_you_know/graphs.html.

Bollobás, B. Graph Theory: An Introductory Course. New York: Springer-Verlag, 1979.

Chartrand, G. Introductory Graph Theory. New York: Dover, 1985.

Foulds, L. R. Graph Theory Applications. New York: Springer-Verlag, 1992.

Chung, F. and Graham, R. Erdos on Graphs: His Legacy of Unsolved Problems. New York: A. K. Peters, 1998.

Gardner, M. ``Graph Theory.'' Ch. 10 in The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 91-103, 1984.

Grossman, I. and Magnus, W. Groups and Their Graphs. Washington, DC: Math. Assoc. Amer., 1965.

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.

Hartsfield, N. and Ringel, G. Pearls in Graph Theory: A Comprehensive Introduction, 2nd ed. San Diego, CA: Academic Press, 1994.

Ore, Ø. Graphs and Their Uses. New York: Random House, 1963.

Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, 1998.

Ruskey, F. ``Information on (Unlabelled) Graphs.'' http://sue.csc.uvic.ca/~cos/inf/grap/GraphInfo.html.

Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, 1986.

Skiena, S. S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Redwood City, CA: Addison-Wesley, 1988.

Trudeau, R. J. Introduction to Graph Theory. New York: Dover, 1994.

Tutte, W. T. Graph Theory as I Have Known It. Oxford, England: Oxford University Press, 1998.