### Domination in Digraphs

### Description

This lecture series will feature eminent local mathematicians or mathematics educators to share with the public some of their interests and ideas.

### Speaker

**Koh Khee Meng, National University of Singapore **

Koh Khee Meng is Professor in the Department of Mathematics at the National University of Singapore (NUS). He graduated from Nanyang University in 1968 and obtained his M.Sc. and Ph.D. from the University of Manitoba in Canada in 1969 and 1971 respectively. Among several other significant appointments, Professor Koh was the chairman of the Singapore International Mathematical Olympiad Committee (1991-93), a council member of the Institute of Combinatorics and Its Applications (International) (1995-97) and the president of the Singapore Mathematical Society (1996-98). He has also won numerous Teaching Awards from the Faculty of Science, NUS. Professor Koh specializes in Combinatorics and Graph Theory and has published more than 150 research articles in international scientific journals. He is co-author of the books: Principles and Techniques in Combinatorics, College Mathematics Volumes 1 & 2, Counting, Chromatic Polynomials and Chromaticity of Graphs and Introduction to Graph Theory-H3 Mathematics.

### Abstract

A vertex w in a digraph D is called an** r-dominating vertex** or **r-king**, where r is a positive integer, if the distance from w to any other vertex in D is at most r. A **tournament** is a digraph in which every two vertices are joined by exactly one arc. In studying dominance relations in certain animal societies, the mathematical sociologist Landau (1953) observed that **every tournament always contains a 2-king.**

In this talk, we begin with this rudimentary observation and follow with some pertaining results. We shall learn how to ask relevant and meaningful questions based on the existing results, and hope that by answering these questions, we may be led to some new discoveries. The whole process of deriving these discoveries will serve to illustrate a way in which research can be fruitfully conducted.

### Audience

General (Suitable for students at JC Level and above)

### Date

March 9 (Wednesday) 2011 / 4.30-5.30pm

### Venue

### Registration Fee

FREE

### Registration

School teachers may do group registration for their students and teachers by choosing the “group registration” option and indicate the number of people attending the lecture in the online registration form.

### Coordinator

Dr Toh Pee Choon