Last week I was at the 8th Slovenian Conference on Graph Theory.  This was the latest in what is commonly known as the ‘Bled conference’ but this year was in Kranjska Gora. This meant that the conference excursion was to Lake Bled. It was a very enjoyable conference with lots of interesting talks and it was good to catch up with lots of people. I was one of the plenary speakers and my talk was entitled ‘Bounding the number of automorphisms of a graph’. This surveyed the recent work on the Weiss conjecture and its generalisation the PSV conjecture. It also discussed my recent work with Luke Morgan on the PSV conjecture for semiprimitive groups with a nilpotent regular normal subgroup.  More details can be found on my slides.

Over the summer break, John and I each supervised a 2nd year undergraduate student in a research project, and the previous post summarised Michael Martis’ project. I supervised Melissa Lee, who learned about the energy of graphs and this is what she did

Hello everyone! My name is Melissa Lee and I’m about to start my third year of Chemical Engineering and Pure Mathematics at UWA. Over these summer holidays, I’ve been given the opportunity to take on a six week research project with Professor Gordon Royle. The area that I have researched is the energy of graphs, with a particular focus on extremal cases. It’s been a new and exciting time for me, being my first experience of research and also my first taste of graph theory.

The idea of the energy of a graph was first introduced by Serbian mathematician Ivan Gutman at a conference in Austria in 1978. Its origins lie in chemistry, where it is defined as “the total $\pi$ electron energy of a conjugated hydrocarbon as calculated with the Hückel Molecular Orbital method”. The concept didn’t receive much attention from mathematicians for many years. However, sometime around the turn of the century, mathematicians realised its value and since then, increasing numbers of papers have been published each year about the energy of graphs.