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arXiv · 1609.04477

Eigenvalue location in cographs

David P. Jacobs·Vilmar Trevisan·Fernando C. Tura
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Abstract

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.

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David P. Jacobs, Vilmar Trevisan, Fernando C. Tura. 2016-09-15. Eigenvalue location in cographs. https://doi.org/10.1016/j.dam.2017.02.007

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