English

Almost all graphs have no cospectral mates with height relative small to its order

Combinatorics 2026-04-28 v2 Spectral Theory

Abstract

The main result of this paper shows that almost all graphs of order nn have no cospectral mates with height o((n/lnn)1/10)o(( n / \ln n)^{1/10}), improving an earlier result on cospectral mates with fixed level and covering the cospectral graphs obtained by GM-switching of relative small blocks.

Keywords

Cite

@article{arxiv.2604.02165,
  title  = {Almost all graphs have no cospectral mates with height relative small to its order},
  author = {Da Zhao},
  journal= {arXiv preprint arXiv:2604.02165},
  year   = {2026}
}