English

Integral cographs and applications

Combinatorics 2019-02-20 v1

Abstract

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we show a cograph that has a balanced cotree TG(a1,,ar1,00,,0,ar)T_{G}(a_{1},\ldots,a_{r-1},0|0,\ldots,0,a_{r}) is integral computing its spectrum. As an application, these integral cographs can be used to estimate the eigenvalues of any cograph.

Keywords

Cite

@article{arxiv.1902.06817,
  title  = {Integral cographs and applications},
  author = {Luiz Emilio Allem and Fernando Tura},
  journal= {arXiv preprint arXiv:1902.06817},
  year   = {2019}
}
R2 v1 2026-06-23T07:44:16.532Z