Coherent Algebras of Trees
Problem: can the pairs of cospectral trees produced by limb swapping have isomorphic coherent algebras?
- Rough notes of CG on coherent and related algebras.
Beating Emms
Problems: The algorithm of Emms et al. fails on some small graphs (quartic on 14, cubic on 16 and 20). Explain why. Does Emms distinguish Latin square graphs?
- A matrix representation of graphs and its spectrum as a graph invariant. Emms, Hancock, Severini, Wilson.
- Quantum walks on regular graphs and eigenvalues. By KG and CG, derives information about eigenvalues of matrices used by Emms.
- Jamie Smith's Ph.D. thesis. Section 4.7 produces an infinite sequence of pairs of graphs (on $k2^{2k-1}$ vertices, $k\ge4$) that beat Emms.
- Krystal Guo's M. Math thesis.
- Some potentially useful code.