International Workshop on Optimal Network Topologies

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International Workshop on Optimal Network Topologies

 17 - 21 Jul 2023

ICMS, Bayes Centre, Edinburgh

Scientific organisers

  • Grahame Erskine, The Open University
  • Patrick Fowler, University of Sheffield
  • Jozef Širáň, The Open University and Slovak Technical University
  • Klara Stokes, Umeå University

About:

The International Workshop on Optimal Network Topologies (IWONT) is an established series of workshops for researchers active in the following areas:

• degree-diameter and degree-girth problems in graphs and digraphs;
• construction techniques and structural properties of optimal graphs and digraphs with given properties;
• spectral techniques in graph theory;
• design of networks for optimal efficiency or reliability;
• applications of graphs to theoretical chemistry.

The principal objective of the workshop was to bring together researchers in the relevant areas to consolidate recent advances, present new results and encourage collaborations on extensions of recent work or new ideas. Among the problem areas where we would expect progress reports or further projects to arise from the meeting are the following:

• 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.

PROGRAMME

Monday 17 July 2023
Registration with tea & coffee
Welcome and programme outline , ICMS staff, IWONT organising committee
Workshop session: Grahame Erskine, The Open University The future of CombinatoricsWiki
Coffee break
Contributed talk: Guillermo Pineda Villavicencio, Deakin University Geometry and the degree-diameter problem
Workshop session Open problems – open to all participants
Lunch
Invited talk: Klara Stokes, Umeå University Sparsity and tightness of hypergraphs and incidence geometries
Contributed talk: Francesc Comellas, Universitat Politècnica de Catalunya Sixty years of the degree-diameter problem
Coffee break
Contributed talk: Willem Haemers, Tilburg University On the spectral characterization of signed graphs
Contributed talk: James Tuite, The Open University Directed and mixed graphs close to the Moore bound
Drinks reception at ICMS
Tuesday 18 July 2023
Invited talk: Gabriela Araujo-Pardo, Mathematics Institute, National University of México On semicubic cages and small graphs of even girth from voltage graphs
Contributed Talk: Martin Macaj, Comenius University Cubic lifts of 2 vertex graphs in the cage problem.
Coffee break
Contributed talk: Aida Abiad, Eindhoven University of Technology, UGent, VUB On eigenvalue bounds for the independence number of graph powers and an application to coding theory
Contributed talk: Nino Bašić, University of Primorska & IMFM On the Nullity of Altans and Iterated Altans
Lunch
Invited talk: Robert Jajcay, Comenius University Upper bounds on the orders of cages
Contributed talk: Štefan Gyürki, Slovak University of Technology On the automorphisms of a family of small $(q,8)$-graphs
Coffee break
Contributed talk: Rob Lewis, The Open University Upper bounds for the order of Abelian Cayley graph families in the degree-diameter problem
Contributed talk: Martin Knor, Slovak University of Technology in Bratislava On metric dimension of circulant graphs
Wednesday 19 July 2023
Invited talk: Rinovia Simanjuntak, Institut Teknologi Bandung Multipartite Ramsey numbers via strongly regular graphs
Contributed Talk: Josep Miret, Universitat de Lleida On the nonexistence of almost Moore digraphs of degree 4 and 5
Coffee break
Contributed talk: Edy Tri Baskoro, Institut Teknologi Bandung On almost Moore digraphs
Contributed talk: Nacho López, Universitat de Lleida Measuring the closeness to mixed Moore graphs
Group photo, then packed lunch & free afternoon
Thursday 20 July 2023
Invited talk: Miguel Ángel Fiol , Universitat Politècnica de Catalunya On the algebra of token graphs
Contributed Talk: Cristina Dalfó, Universitat de Lleida On the spectra and spectral radii of token graphs
Coffee break
Contributed talk: Mónica Reyes , Universitat de Lleida A general method to find the spectrum and eigenspaces of the k-token graph of a cycle
Contributed talk: David Wilsch , Comenius University in Bratislava McKay–Miller–Širáň graphs are lifts of dipoles
Lunch
Invited talk: Patrick W Fowler, University of Sheffield Graph theory for molecular currents: conduction and aromaticity
Contributed talk: David Whittaker, University of Sheffield Experimental topological physics with coaxial cable networks
Coffee break
Contributed talk: Maxine McCarthy, University of Sheffield Measuring spectral properties of nut graphs with coaxial cable networks
Contributed talk: Tatiana Jajcayová, Comenius University Totally regular mixed graphs constructed from CD(n,q) graphs of Lazebnik, Ustimenko and Woldar
Conference Dinner
Friday 21 July 2023
Invited talk: Felix Lazebnik, University of Delaware Some families of algebraically defined graphs and their applications
Contributed Talk: Vasyl Ustimenko, Royal Holloway University of London On families of homogeneous algebraic graphs of large girth
Coffee break
Contributed talk: Primož Potočnik, University of Ljubljana Cycle-regularity in vertex-transitive graphs
Contributed talk: Jozef Rajnik, Comenius University Bratislava Cyclic connectivity of cages
Lunch and end of workshop