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math.CO2024
The Hoffman program for mixed graphs
Yuantian Yu, Edwin R. van Dam
We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all mixed graphs without…
math.CO2024
Characterizations of amorphic schemes and fusions of pairs
Edwin R. van Dam, Jack H. Koolen, Yanzhen Xiong
An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a…
math.CO2024
Rainbow Hamiltonicity and the spectral radius
Yuke Zhang, Edwin R. van Dam
Let be a family of graphs of order with the same vertex set. A rainbow Hamiltonian cycle in is a cycle that visits each vertex p…