Photo Credit: Gary Chartrand, Chira Lumduanhom
Photo Credit: Ping Zhang, Rebecca Powers
An interview with Arthur Benjamin, Gary Chartrand & Ping Zhang, coauthors of The Fascinating World of Graph Theory
What is graph theory?
Graph theory is the study of objects, some pairs of which are related in some manner. Since there are no restrictions on what the objects might be and no restrictions on how two objects might be related, applications of graph theory are only limited by one’s imagination.
Why is graph theory important?
There are problems and questions that occur in a wide variety of settings that can be visualized with the aid of graphs and which can often be understood more clearly. Understanding the theoretical nature of graph theory can, in many instances, lead us to solutions of these problems and answers to these questions.
Where do you see graph theory in action in the real world?
Because graph theory has been shown to be so useful with problems in transportation, communication, chemistry, computer science, decision-making, games and puzzles, among other things, there are few aspects of life where graphs do not enter in.
Who needs to understand graph theory? And why does understanding the theoretical underpinnings help us?
Whether it’s mathematics or some other scholarly endeavor, a key element to understanding is not only becoming aware of what others have accomplished but developing a knack of being curious and asking relevant questions. Because graph theory has applications in so many areas, it is an ideal area within mathematics to become familiar with.
Why did you write this book?
There have been numerous reports of American students doing poorly in mathematics in recent years. Furthermore, we believe that mathematics has acquired an under-served reputation of being boring and difficult. While gaining a good understanding of any subject requires effort, we know that many aspects of mathematics are interesting. Since we felt it was likely that many people are not familiar with graph theory, we decided to illustrate how interesting and useful mathematics can be by writing a book on graph theory with this goal in mind. While we wanted to include some real mathematics, showing how certain facts can be verified, we primarily wanted to show where mathematics comes from, discussing some of the people responsible for this, and how mathematics can assist us, often in many unexpected and fascinating ways.