April has been a very busy month for me for various reasons. One of them is that I had three preprints put on the arXiv: Let me discuss all of these here with a focus on the first of the three. In each case I try to focus on aspects which are not the focus […]
One of the greatest discovery of in the theory of distance-regular graphs has been the twisted Grassmann graph by Edwin van Dam and Jack Koolen. Here I want to describe a small variation of their construction for the twisted $ {D_{5,5}(q)}$ graph. This post mostly to preserve my blackboard on the topic. (I tend to […]
Apparently, I described a very elegant argument to give a lower bound on the second largest eigenvalue of the adjacency matrix of a regular graph last year. This was pointed out in two recent preprints by Eero Räty, Benny Sudakov, and Istvan Tomon. This blog post is to describe the very short argument and how […]
Today I write about a recent hobby of mine: Collecting strongly regular graphs. It started three years ago. You can find my collection on my homepage. I collect many SRGs with known parameters. It started here. This is about size, not quantity, and tries to give an idea how a typical SRG with certain parameters […]
One of the structures investigated in finite geometry are related to quadratic forms over finite fields (see below for definitions). Knowledge on the geometry of singular points of quadratic forms is very common and covered in many textbooks on finite geometry, but one cannot say the same for the geometry on non-singular points. This short […]
Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36, 10, 4, 2), but there are 32548 non-isomorphic graphs with parameters (36, 15, 6, 6). Peter Cameron, Random Strongly Regular Graphs? This a shorter version of this report which I just […]