English

Eigenvalue location in cographs

Combinatorics 2017-04-05 v1

Abstract

We give an O(n)O(n) time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and xRx\in \mathbb{R}. Applications include determining the number of eigenvalues of a cograph's adjacency matrix that lie in any interval, obtaining a formula for the inertia of a cograph, and exhibiting infinitely many pairs of equienergetic cographs with integer energy.

Keywords

Cite

@article{arxiv.1609.04477,
  title  = {Eigenvalue location in cographs},
  author = {David P. Jacobs and Vilmar Trevisan and Fernando C. Tura},
  journal= {arXiv preprint arXiv:1609.04477},
  year   = {2017}
}
R2 v1 2026-06-22T15:50:14.128Z