Eigenvalue location in cographs
Copyright policy )Eigenvalue location in cographs
We give an $O(n)$ time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and $x\in \mathbb{R}$. 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.
- Federal University of Rio de Janeiro Brazil
- Clemson University United States
- Universidade Federal de Santa Maria Brazil
adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), FOS: Mathematics, eigenvalue, Mathematics - Combinatorics, 05C50, 05C85, 15A18, Combinatorics (math.CO), cograph
adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), FOS: Mathematics, eigenvalue, Mathematics - Combinatorics, 05C50, 05C85, 15A18, Combinatorics (math.CO), cograph
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).17 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!