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math.CO2026
Almost all graphs are determined by their generalized spectrum
Ziqing Xiang
Haemers' conjecture for the generalized spectrum asserts that almost all graphs are determined by their generalized spectrum, that is, for almost all graphs , every graph with t…
math.CO2026
Permutation automorphism groups of cyclic codes I: cyclotomic association schemes
Yanni Wu, Ziqing Xiang
The Berger-Charpin conjecture predicts that the permutation automorphism group of a cyclic code is generally the -affine group, which is generated by the shift and the Frobenius…
math.CO2026
Natural graph spectra
Ziqing Xiang
In 2003, van Dam and Haemers posed a fundamental question in spectral graph theory: does there exist a ``sensible'' matrix whose spectrum determines a random graph up to isomorphis…