International Workshop on Optimal Network Topologies

Grahame Erskine has secured a £24,000 grant from the International Centre for Mathematical Sciences to hold the International Workshop on Optimal Network Topologies 2023 (IWONT 2023). The workshop will be organised by Grahame along with Patrick Fowler (University of Sheffield), Jozef Širáň (The Open University and Slovak Technical University), and Klara Stokes (Umeå University). The previous workshop of the same name was IWONT 2016, held at the Tsinghua Sanya International Mathematics Forum, 2016. Participants from that meeting are shown in the photo.

Some of the topics to be considered at IWONT 2023 are as follows.

• Existence of Moore graphs; not only the well-known open problem at degree 57 but also mixed graphs, where there are an infinity of open cases and much interest in recent years.
• Upper or lower bounds on the possible defect (in the diameter problem) or excess (in the girth problem) where Moore graphs are known not to exist.
• Restricted problems, such as optimal Cayley graphs or vertex-transitive graphs, bipartite graphs, graphs embeddable on surfaces of given genus and so on.
• Analogues of the girth problem on undirected graphs, such as extensions to digraphs, mixed graphs and hypergraphs and related concepts such as geodecity.