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math.CO2026
On applications of the clique-adjacency polynomial to arbitrary finite graphs
Jake Rigg, John Bamberg
The clique adjacency polynomial (CAP), introduced by Soicher (2015), provides a powerful method for bounding the clique numbers of edge-regular graphs. In this paper, we extend the…
math.CO2024
The synchronisation hierarchy via coherent configurations
John Bamberg, Jesse Lansdown
We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating…
math.CO2021
Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry
John Bamberg, Jesse Lansdown
In this paper we show that if is a -design of an association scheme , and the Krein parameters vanish for some and all $i, j \no…