Eigenvalue location in graphs of small clique-width

Martin Fürer; Carlos Hoppen; David P. Jacobs; Vilmar Trevisan

doi:10.1016/j.laa.2018.09.015

Eigenvalue location in graphs of small clique-width

Martin Fürer
, Carlos Hoppen
, David P. Jacobs
, Vilmar Trevisan

Eberly College of Science

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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	https://doi.org/10.1016/j.laa.2018.09.015
State	Published - Jan 1 2019

All Science Journal Classification (ASJC) codes

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

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10.1016/j.laa.2018.09.015

Cite this

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title = "Eigenvalue location in graphs of small clique-width",

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.",

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AU - Fürer, 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.

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UR - https://www.scopus.com/pages/publications/85053827442#tab=citedBy

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DO - 10.1016/j.laa.2018.09.015

M3 - Article

AN - SCOPUS:85053827442

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SP - 56

EP - 85

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Eigenvalue location in graphs of small clique-width

Abstract

All Science Journal Classification (ASJC) codes

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