The Homepage of Dr Ng Kah Loon

I can be reached at S14-05-06 Department of Mathematics 2 Science Drive 2 Singapore 117543 Email address: matngkl@nus.edu.sg

Useful Links Current Teaching Duty (MA 1508 Course Homepage) NUS Homepage Faculty of Science Homepage Department of Mathematics DIMACS (Center of Discrete Mathematics and Theoretical Computer Science, New Jersey) InForMID (Tufts Initiative Initiative for the Forecasting and Modeling of Infectious Diseases)

About myself: I was appointed as Teaching Assistant with the Department of Mathematics in January 2000. However, my acquaintance with the Department started way back in July 1994, when I matriculated as an undergraduate. After spending 5 years and obtaining 3 degrees in the process, I left the University in July 1999 to work with Singapore Airlines as a..........(Air Steward? You must be joking!) : )

I was actually a Revenue Technology Analyst with the Airline, putting my education in Mathematics, in particular the area of Optimization to good use. My time with SIA turned out to be short but nevertheless fulfilling. My liking for Graph Theory and the desire to pursue a higher degree brought me back to the Department. From January 2000 to May 2004, I worked on my PhD under the supervision of Professor Koh Khee Meng. I submitted my thesis entitled "A New Direction in the Study of the Orientation Number of a Graph" in June 2004 and was conferred the degree of Doctor of Philosophy in October 2004.

I was then awarded a visiting fellowship by the National University of Singapore in September 2004 and proceeded to DIMACS (Center of Discrete Mathematics and Theoretical Computer Science) in Rutgers University, New Jersey, United States. Since September 2004, I have been a postdoctoral fellow here at DIMACS. It is expected that I will remain at DIMACS until 2006 before I return to the Department of Mathematics, NUS.

Jan 2007: I have returned! I am now back with the Department of Mathematics after two fruitful years in the United States. My first teaching assignment in Jan 2007 is a ESP (Engineering Science Program) module MA1508 - Linear Algebra with Applications.

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My teaching duties since January 2000:
 

My area of Research:Graph Theory

Leonhard Euler (1707-1783)

While mathematics has a long and glorious history, this is not the case of the mathematical area of graph theory. Oystein Ore, the prominent number theorist and graph theorist and author of the first graph theory book written in English said that

    ".....the theory of graphs is one of the few fields of mathematics with a definite birth date........."

Graph theory is considered to have begun in 1736 with the publication of Euler's (above) solution of the Konigsberg Bridge Problem. Two hundred years later, in 1936, Denes Konig (1884-1944) wrote the first book on graph theory. In the relative short period since then, the major developments of graph theory have occurred, inspired, to a large degree, by the ever-growing importance of computer science and its connection with graph theory.

There are many interesting problems on which the theory of graphs can be applied to. Some examples are:

• How can the season of a sports league be scheduled into the minimum number of weeks?
• In what order should a travelling salesman visit cities to minimize travel time?
• Can we colour the regions of every map using four colours so that neighbouring regions receive different colours?
• What is maximum flow per unit time from source to sink in a network of pipes?

For those interested, I recommend you the following books on graph theory which are both elementary and interesting. They are available for loan from the University's Science libray. Enjoy and have fun!

[1] Graphs as mathematical models by Gary Chartrand. Prindle, Weber & Schmidt, 1977.

[2] Introduction to Graph Theory by Douglas B. West. Prentice Hall, 1996.

[3] Graphs and Digraphs (3rd Edition) by Gary Chartrand and Linda Lesniak. Chapman & Hall, 1996.

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Publications:

1. H. Aslaksen and K.L Ng, The Graduate Tutor Training Workshop in the Department of Mathematics, CDTL Brief, Center for Development of Teaching and Learning, National University of Singapore, 6 (2003), no. 6, 11-12. (html)
2. K.M. Koh and K.L. Ng, The Orientation Number of Two Complete Graphs with Linkages, Discrete Mathematics, 295 (2005), 91-106. (pdf)
3. K.L. Ng and P. Raff, A Generalization of the Firefighter Problem, DIMACS Technical Report, 2005-23 (2005), Rutgers University. (pdf)
4. K.M. Koh and K.L. Ng, On Optimal Orientation of Cycle Vertex-multiplications, Discrete Mathematics, in print.
5. K.L. Ng, On a Conjecture Concerning the Orientation Number of a Graph, Discrete Mathematics, submitted.
6. K.L. Ng and P. Raff, Fractional Firefighting in the Two Dimensional Grid, Journal of Combinatorial Mathematics and Combinatorial Computing, submitted.  (C Code)