Publications

A graph energy conjecture through the lenses of semidefinite programming

A Abiad, G Coutinho, E Juliano, H. Reijnders

SIAM Journal on OptimizationAcceptedarXivBibTeXCite

A lifted entropy splitting lemma and applications

G Coutinho, L Higino

PreprintarXivBibTeXCite

A Lovász Theta Parameter and Theta Body for Signed Graphs

G Coutinho

PreprintarXivBibTeXCite

A SWAP-free Framework for QAOA

T Assis, P Baptista, L Lopes, D Ferreira, G Coutinho

PreprintarXivBibTeXCite

Clique and chromatic numbers of graph powers: spectral bounds and anticodes

A Abiad, G Coutinho, H Kumar, E Juliano, M Tait

PreprintarXivBibTeXCite

Compact graphs and quantum automorphisms

P Baptista, G Coutinho, C Godsil, S Schmidt

PreprintarXivBibTeXCite

Computing fixed point free automorphisms of graphs

A Abiad, G Coutinho, E Juliano, V dos Santos, S Zeijlemaker

LATIN 2026AcceptedarXivBibTeXCite

Conference version accepted at LATIN 2026; journal version submitted.

On some k-fold generalizations of Lovász theta and their sandwich theorems

MKC Silva, G Coutinho, T Oliveira, L Tunçel

PreprintarXivBibTeXCite

Semidefinite programming bounds on fractional cut-cover and maximum 2-SAT for highly regular graphs

H Assumpção, G Coutinho

Mathematics of Operations Research 2026DOIarXivBibTeXCite

Total Conformal Rigidity in Graphs

H Assumpção, G Coutinho, C Godsil

PreprintarXivBibTeXCite

Two chromatic numbers, eigenvalues and a generalized Lovász theta

MK Silva, G Coutinho, R Grandsire

Special Matrices 14(1), 20250060 (2026)DOIarXivBibTeXCite

Zero-freeness of a multivariate monomer-dimer-cycle polynomial on bounded-degree graphs

G Coutinho, PMS Fialho

PreprintarXivBibTeXCite

A connection between the Aα-spectrum and the Lovász theta number

G Coutinho, T Oliveira

Linear Algebra and Its Applications 2025arXivPaperBibTeXCite

Orthogonal polynomials, quantum walks and the Prouhet–Tarry–Escott problem

F Cançado, G Coutinho, TJ Spier

PreprintarXivBibTeXCite

Peak state transfer in continuous quantum walks

G Coutinho, K Guo, V Schmeits

PreprintarXivBibTeXCite

Spectral upper bounds for the Grundy number of a graph

T Assis, G Coutinho, E Juliano

Discrete Mathematics 348(3), 114326 (2025)DOIarXivBibTeXCite

The spectrum of symmetric decorated paths

G Coutinho, E Juliano, TJ Spier

Linear Algebra and Its Applications 2025arXivPaperBibTeXCite

Unsupervised Hierarchical Sequence Stratigraphy Framework of Carbonate Successions

MVS Dantas, KHM Vieira, TJ Spier, JAO Santos, ACT Prado, D Vomlel, M Leite, FA Farias, DGC Fragoso, H Reis, G Coutinho, DG Macharet

Artificial Inteligence in Geosciences 2025PaperBibTeXCite

Conic programming to understand sums of squares of eigenvalues of graphs

G Coutinho, TJ Spier, S Zhang

PreprintarXivBibTeXCite

(this paper heavily supersedes the earlier preprint by Thomás and I)

No perfect state transfer in trees with more than 3 vertices

G Coutinho, E Juliano, TJ Spier

Journal of Combinatorial Theory Series B 2024DOIarXivBibTeXCite

Quotient graphs and stochastic matrices

F Cançado, G Coutinho

PreprintarXivBibTeXCite

Selected Open Problems in Continuous-Time Quantum Walks

G Coutinho, K Guo

Special Matrices 2024DOIarXivBibTeXCite

Unexpected Averages of Mixing Matrices

P Baptista, G Coutinho, V Marques

Quantum Information Processing 2024DOIarXivBibTeXCite

Constructing high-resolution stratigraphic frameworks by the application of signal analysis techniques: Example of Balbuena IV Sequence, Yacoraite Formation, Salta Basin

JAO Santos, A Uhlein, MVS Dantas, G Coutinho, TJ Spier, KHM Vieira, ACT Prado, D Macharet, GJ Uhlein, T Novo, H Reis, FA Farias, EB Freire, DGC Fragoso

Marine and Petroleum Geology 2023PaperBibTeXCite

Irrational quantum walks

G Coutinho, PF Baptista, C Godsil, TJ Spier, R Werner

SIAM Journal of Applied Algebra and Geometry 2023DOIarXivBibTeXCite

Quantum Walks in the Normalized Laplacian

G Coutinho, PF Baptista

Linear and Multilinear Algebra 2023DOIarXivBibTeXCite

Strong cospectrality in trees

G Coutinho, E Juliano, TJ Spier

Algebraic Combinatorics 2023DOIarXivBibTeXCite

Why and how to add direction to a quantum walk

R Chaves, BO Chagas, G Coutinho

Quantum Information Processing 2023DOIarXivBibTeXCite

A novel reconstruction attack on foreign-trade official statistics, with a Brazilian case study

DF Favato, G Coutinho, MS Alvim, N Fernandes

PoPETS 2022arXivPaperBibTeXCite

Fundamentals of fractional revival in graphs

A Chan, G Coutinho, W Drazen, O Eisenberg, C Godsil, M Kempton, G Lippner, C Tamon, H Zhan

Linear Algebra and its Applications 655 (2022), 129–158DOIarXivBibTeXCite

Optimization of eigenvalue bounds for the independence and chromatic number of graph powers

A Abiad, G Coutinho, MA Fiol, BD Nogueira, S Zeijlemaker

Discrete Mathematics 2022arXivPaperBibTeXCite

Quantum walks do not like bridges

G Coutinho, C Godsil, E Juliano, CM van Bommel

Linear Algebra and Its Applications 2022arXivPaperBibTeXCite

Dual Hoffman Bounds for the Stability and Chromatic Numbers Based on Semidefinite Programming

NB Proença, MK de Carli Silva, G Coutinho

SIAM Journal on Discrete Mathematics 2021DOIarXivBibTeXCite

Fractional revival and association schemes

A Chan, G Coutinho, C Tamon, L Vinet, H Zhan

Discrete Mathematics 2020arXivPaperBibTeXCite

Algebras, graphs and thetas

MK de Carli Silva, G Coutinho, C Godsil, DE Roberson

LAGOS 2019arXivPaperBibTeXCite

Colouring the normalized Laplacian

G Coutinho, R Grandsire, C Passos

LAGOS 2019arXivPaperBibTeXCite

Discretization of continuous-time quantum walks via the staggered model with Hamiltonians

G Coutinho, R Portugal

Natural Computing 2019DOIarXivBibTeXCite

On the k-independence number of graphs

A Abiad, G Coutinho, MA Fiol

Discrete Mathematics 2019arXivPaperBibTeXCite

Perfect state transfer in a spin chain without mirror symmetry

G Coutinho, L Vinet, H Zhan, A Zhedanov

Journal of Physics A: Mathematical and Theoretical 2019DOIarXivBibTeXCite

Quantum fractional revival on graphs

A Chan, G Coutinho, C Tamon, L Vinet, H Zhan

Discrete Applied Mathematics 2019arXivPaperBibTeXCite

Quantum walks and the size of the graph

G Coutinho

Discrete Mathematics 2019arXivPaperBibTeXCite

A New Perspective on the Average Mixing Matrix

G Coutinho, C Godsil, K Guo, H Zhan

The Electronic Journal of Combinatorics 2018arXivPaperBibTeXCite

Continuous-Time Quantum Walks in Graphs

G Coutinho, C Godsil

IMAGE — The Bulletin of the International Linear Algebra Society 60 (2018), 12–21PaperBibTeXCite

Perfect state transfer is poly-time

G Coutinho, C Godsil

Quantum Information & Computation 2017arXivPaperBibTeXCite

Pretty good state transfer between internal nodes of paths

G Coutinho, K Guo, CM van Bommel

Quantum Information & Computation 2017DOIarXivBibTeXCite

Pretty good state transfer in qubit chains—The Heisenberg Hamiltonian

L Banchi, G Coutinho, C Godsil, S Severini

Journal of Mathematical Physics 2017DOIarXivBibTeXCite

Equiangular Lines and Covers of the Complete Graph

G Coutinho, C Godsil, M Shirazi, H Zhan

Linear Algebra and Its Applications 2016arXivPaperBibTeXCite

Perfect state transfer in products and covers of graphs

G Coutinho, C Godsil

Linear and Multilinear Algebra 2016DOIarXivBibTeXCite

Spectrally extremal vertices, strong cospectrality, and state transfer

G Coutinho

The Electronic Journal of Combinatorics 2016arXivPaperBibTeXCite

No Laplacian Perfect State Transfer in Trees

G Coutinho, H Liu

SIAM Journal of Discrete Mathematics 2015DOIarXivBibTeXCite

Perfect state transfer on distance-regular graphs and association schemes

G Coutinho, C Godsil, K Guo, F Vanhove

Linear Algebra and its Applications 478 (2015), 108–130DOIarXivBibTeXCite