### Abstract

Finding a diagonal matrix congruent to A−cI for constants c, where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval. If G has clique-width k and a corresponding k-expression is known, then diagonalization can be done in time O(poly(k)n) where n is the order of G.

Original language | English (US) |
---|---|

Pages (from-to) | 56-85 |

Number of pages | 30 |

Journal | Linear Algebra and Its Applications |

Volume | 560 |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

### Cite this

*Linear Algebra and Its Applications*,

*560*, 56-85. https://doi.org/10.1016/j.laa.2018.09.015

}

*Linear Algebra and Its Applications*, vol. 560, pp. 56-85. https://doi.org/10.1016/j.laa.2018.09.015

**Eigenvalue location in graphs of small clique-width.** / Furer, Martin; Hoppen, Carlos; Jacobs, David P.; Trevisan, Vilmar.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Eigenvalue location in graphs of small clique-width

AU - Furer, Martin

AU - Hoppen, Carlos

AU - Jacobs, David P.

AU - Trevisan, Vilmar

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Finding a diagonal matrix congruent to A−cI for constants c, where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval. If G has clique-width k and a corresponding k-expression is known, then diagonalization can be done in time O(poly(k)n) where n is the order of G.

AB - Finding a diagonal matrix congruent to A−cI for constants c, where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval. If G has clique-width k and a corresponding k-expression is known, then diagonalization can be done in time O(poly(k)n) where n is the order of G.

UR - http://www.scopus.com/inward/record.url?scp=85053827442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053827442&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.09.015

DO - 10.1016/j.laa.2018.09.015

M3 - Article

VL - 560

SP - 56

EP - 85

JO - Linear Algebra and Its Applications

T2 - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -