The so-called “Foster Census” of cubic symmetric graphs (networks) has been very ably continued by New Zealand mathematician Professor Marston Conder. In August last year, he gave us a complete list of cubic symmetric graphs on up to 10,000 vertices. The chart above summarises that list, noting the diameter, girth, and order (number of vertices) of each graph. Each coloured dot is a graph. Seven of the better-known graphs are labelled, and the Tutte–Coxeter graph is illustrated (click on the chart for a larger image).
The University of Auckland: it’s not just fantastic movies that come out of New Zealand!