CS 503

Information to Graduate Students


CS 503 APPLIED GRAPH THEORY

(to be offered next time in Fall 2011)

(This course is recommended as an entry-level graduate course. )

Prerequisite: Graduate standing (working knowledge in linear algebra, matrix theory and linear equations, such as those discussed in Math 310 - Applied Linear Algebra) or consent of Instructor

Text: T. Murata, "Applied Graph Theory" (Lecture Notes for CS 503) and a reprint of some chapters from N. Deo, "Graph Theory with Applications to Engineering and Computer Science," Prentice Hall. It will be made available at the UIC Book Store during the first week of Semester.

References (optional): G. Chartrand and L. Lesniak, "Graphs & Digraphs," 4th ed., CRC Press, 2005. J. Gross and J. Yellen, "Graph Theory and its Applications," CRC Press, 1999.

Course Grades are in general based on two exams, home works, and a report.

Topics (subject to change):

1 Introduction: historical notes, basic terminology, graph synthesis examples

2 Paths and circuits: Hamiltonian paths, Euler graphs, operations on graphs

3 Trees: spanning trees, their properties, theorems and proofs; distance, eccentricity, radius, diameter; f-circuits, elementary tree transformation, finding all spanning trees

4 Cutsets: f-cutsets, measures of connectivity, separable graphs, Menger's theorem, maximum-flow/minimum-cut theorem, network flows, terminal capacity matrix, synthesis of communication nets

5 Planar and dual graphs: Euler's formula, geometric and combinatorial duals, theorems of Kuratowski, Whitney and MacLane

6 Vector space of a graph: circuit and cutset subspaces, orthogonality, other subspaces

7 Matrix representation of graphs: relationships and properties of incidence-, cutset-, circuit- and path-matrices

8 Synthesis of (Boolean) switching networks, odd-ring sum condition, Tutte realizability

9 Coloring, dominating sets, minimum covers, partitioning, maximum matching

10 Directed graphs, strongly connected graphs, out-trees, in-trees, matrices for directed graphs, Binet-Cauchy theorem, Kirchohoff matrix, properties of acyclic graphs

11 NP-complete graph and network problems

Most Frequently Asked Questions:

Q1 Where is this course useful?: Many systems, concepts, and problems in Computer Science and Engineering can be modeled or expressed as graphs (such as trees, path, ....), and graph problems (such as "Find the shortest tree, shortest path, etc.") Thus it is "useful" to know what kinds of things we can do with graph theory, once they are modeled as graphs and graph problems.

Q2 Related areas are: Discrete Mathematics, Algorithms, Data Structure, and Modeling and Analysis of Concurrent Systems (CS 554).

Just as any undergraduate curriculum in CS or ECE starts with some math courses, it is advisable to include some math type of courses such as applied graph theory in the graduate curriculum. In this sense, this course is recommended as an entry-level graduate course.

For further information or question, contact Professor Murata at (312)996-2307 or e-mail to murata@uic.edu.