Regarded as a world leader in domination theory in graphs, Prof Henning, obtained his PhD at the University of Natal in April 1989. He started his academic career as a lecturer at the University of Zululand, before accepting a lectureship in mathematics at the former University of Natal in January 1991. In January 2000, Prof Henning was appointed a Full Professor at the University of Natal, which later merged with the University of Durban-Westville to form the University of KwaZulu-Natal in January 2004. After spending almost 20 years at the University of KwaZulu-Natal and one of its predecessors, the University of Natal, Prof Henning moved to UJ in May 2010 as a research professor.

Prof Henning’s research interests are in the field of graph theory which is a major area of combinatorics. He has made significant contributions to several topics in graph theory and hypergraph theory including colorings, matchings, independence, domination theory, identifying codes, transversals, and digraphs. Prof Henning is regarded as a world-leader in domination theory in graphs. Over the last few years, Prof Henning has combined forces with Professor Anders Yeo, currently at the Singapore University of Technology and Design, and they have focused their research on the interplay of total domination in graphs and transversals in hypergraphs. Prof Henning and Prof Yeo recently co-authored a book in 2013 entitled “Total domination in graphs” (Springer Monographs in Mathematics).

Prof Henning was awarded an international award, a Hall Medal, in 2000 that “recognises outstanding research achievements by members of the Institute of Combinatorics and its Applications who are not over age 40″. Only two Hall Medals were awarded in 2000, the other recipient being an Australian mathematician. In 2009, he was the recipient of a National Research Foundation A-rating which is reserved for “researchers who are unequivocally recognised by their peers as leading international scholars in their field for the high quality and impact of their recent research outputs.” The rating is valid for the period 2009-2014.

Prof Henning has been a plenary and invited speaker at several international conferences in countries such as the USA, Germany, France, Poland, and Slovakia. He is a prolific researcher having published over 320 papers to date in international mathematics journals. He has over 3,700 journal citations to his articles. He serves as a section editor of five international journals, including co-managing editor of the Japanese based journal Graphs and Combinatorics.​

The University of Johannesburg, and one of its predecessors the Rand Afrikaans University, has an established footprint in graph theory developed over four decades. In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A graph is a finite nonempty set of objects called vertices together with a (possibly empty) set of unordered pairs of distinct vertices called edges. The basic concepts of graph theory are extraordinarily simple but can be used to express problems from many different subjects. Graph theory can be used in the planning of such prosaic systems as traffic-light networks, mail delivery, and rubbish collection routes. It is used in town planning to find the best locations for service or emergency facilities.

One of the showpieces of real-world applications of graph theory is public transportation and GPS car navigation systems.

Although graph theory came into existence during the first half of the 18th century, during recent decades the subject has exploded and has developed into a major area of mathematics partly due to its real-world applications. However, it is the beauty of graph theory that has attracted so many to it. Graph theory, more than any other branch of mathematics feeds on problems. In contrast to most traditional branches of mathematics, an unsolved or open” problem in graph theory is often easy to state, but may still take years to solve without any guarantee of a solution.

In this address we introduce the basic concepts of graph theory and show that graph theory is everywhere! We discuss some applications of graphs, including the Chinese Postman Problem, GPS car navigation systems, the Travelling Salesman Problem, and the Instant Insanity Problem.