Aida Abiad

Welcome to my homepage!

I am a tenured assistant professor at Eindhoven University of Technology (TU/e), where I am part of the Department of Mathematics and Computer Science.

I am also a research fellow at the Department of Mathematics: Analysis, Logic and Discrete Mathematics at Ghent University and at the Department of Mathematics and Data Science of Vrije Universiteit Brussel, supported by a personal research FWO fellowship.

arXiv • Google Scholar • dblp

a.abiad.monge *at* tue.nl / aida.abiad *at* ugent.be

Eindhoven University of Technology

Department of Mathematics and Computer Science

MF 4.106

Postbus 513

5600MB Eindhoven

The Netherlands

### Research

I work primarly in algebraic graph theory. I am for example interested in studying which properties of a graph can be deduced from its spectrum. My research interests also include combinatorial optimization, quantum information theory and finite geometry.

### Algebraic Graph Theory group at TU/e

**1-year p****ostdoc vacancy in Algebraic Combinatorics TU/e**** **

Maarten de Boeck (postdoc TU/e, 2020-2022)

Sjanne Zeijlemaker (PhD student TU/e, 2020-2024)

Antonina Khramova (PhD student TU/e, 2021-2025)

Robin Simoens (master student UGent, 2021-2022)

Amber Manders (master student TU/e, 2021-2022)

Nick Reiniers (master student TU/e, 2021-2022)

David Tuin (master student TU/e, 2021-2022)

### Grants

NWO KLEIN-1 Grant (2021-2025)

FWO Senior Postdoctoral Fellowship (2020-2023)

BOF Junior Postdoctoral Fellowship (2018-2021)

### Editorial

Associate editor Computational and Applied Mathematics

### Publications and preprints

**32****.**** ****An infinite class of Neumaier graphs and non-existence results** (arXiv)

(with W. Castryck, M. De Boeck, J. H. Koolen and S. Zeijlemaker)

**31. ****On inertia and ratio type bounds for the k-independence number of a graph and their relationship** (arXiv)

(with C. Dalfó, M.A. Fiol and S. Zeijlemaker)

**30. Constructions of cospectral graphs with different zero forcing numbers** (arXiv)

(with B. Brimkov, J. Breen, T.R. Cameron, H. Gupta, R. Villagran)

**29****. ****A bound for the p-domination number of a graph in terms of its eigenvalue multiplicities **(arXiv)

(with S. Akbari, M.H. Fakharan and A. Mehdizadeh)

**2****8****. ****Characterizing and computing weight-equitable partitions of graph****s** (arXiv)

(with C. Hojny and S. Zeijlemaker)

**2****7****. Spectral upper bound on the quantum k-independence number of a graph** (arXiv)

(with C. Elphick and P. Wocjan)

**2****6****. Eigenvalues, Smith normal form and determinantal ideals** (arXiv)

(with C. Alfaro, K. Heysse and M.C. Vargas)

**25. Optimization of eigenvalue bounds for the independence and chromatic number of graph powers** (journal), *Discrete Math.* 345(3) (2022)

(with G. Coutinho, M.A. Fiol, B.D. Nogueira and S. Zeijlemaker)

**2****4****. Coloring the normalized Laplacian for oriented hypergraphs** (journal), *Linear Algebra and Appl. *629 (2021), 192-207

(with R. Mulas and D. Zhang)

**23. The Kaledoiscopic Game of Life** (journal), *Complex Systems* 31 (2022).

(with M. Geldmacher and A. Grigoriev)

**22. Enumeration of cospectral and coinvariant graphs** (journal), *Applied Mathematics and Computation *408 (2021)

(with C. Alfaro)

**21. Neumaier graphs with few eigenvalues **(journal), *Des. Codes Crypt.* (2021)

(with B. De Bruyn, J. D'haeseleer and J. H.Koolen)

**20. On the status sequences of trees** (journal), *Theoretical Computer Science* 856 (2021), 110-120

(with B. Brimkov and A. Grigoriev)

**19. Printed Circuit Boards Isomorphism: an Experimental Study** (journal), *Computers&Industrial Engineering *148 (2020)

(with A. Grigoriev and S. Niemzok)

**18. On the complexity of solving a decision problem with flow-depending costs: the case of the IJsselmeer dikes** (journal), *Discrete Opt.* 37 (2020)

(with S. Gribling, D. Lahaye, M. Mnich, G. Regts, L. Vena, G. Verweij and P. Zwaneveld)

**17. A characterization and an application of weight-regular partitions of graphs** (journal), *Linear Algebra and Appl.* 569 (2019), 164-174

**16. Graph switching, 2-ranks, and graphical Hadamard matrices** (journal), *Discrete Math.* 342(10) (2019), 2850-2855

(with S. Butler and W.H. Haemers)

**15. On the k-independence number of graphs **(journal), *Discrete Math.* 342(10) (2019), 2875-2885

(with G. Coutinho and M.A. Fiol)

**14. Spectral bounds for the connectivity of regular graphs of given order** (journal), *Electron. J. Linear Algebra *34 (2018), 428-443

(with B. Brimkov, X. Martínez-Rivera, J. Zhang and S. O)

**13. Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree **(journal), *Electron. J. Linear Algebra *34 (2018), 373-380

(with G. Aalipour, Z. Berikkyzy, L. Hogben, F.H.J. Kenter, J.C.-H. Lin and M. Tait)

**12. On the Wiener index, distance cospectrality and transmission regular graphs** (journal), *Discrete Appl Math. *230 (2017), 1-10

(with B. Brimkov, A. Erey, L. Leshock, X. Martínez-Rivera, S. O, S.-Y. Song and J. Williford)

**11. An application of Hoffman graphs for spectral characterizations of graphs** (journal), *Electron. J. Comb. *24(1) (2017)

(with Q. Yang and J.H. Koolen)

**10. Spectral bounds for the k-independence number of a graph **(journal), *Linear Algebra and Appl. *510 (2016), 160-170

(with S. Cioaba and M. Tait)

**9. On the Distance Spectra of Graphs** (journal), *Linear Algebra and Appl. *497 (2016), 66-87

(with G. Aalipour, Z. Berikkyzy, J. Cummings, J. De Silva, W. Gaok, K. Heysse, L. Hogben, F.H.J. Kentery, J.C.-H. Lin, and M. Tait)

**8. Switched symplectic graphs and their 2-ranks** (journal), *Des. Codes Crypt.* 81(1) (2016), 35-41

(with W.H. Haemers)

**7. Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs **(journal), *J. Combin. Theory Ser. A *143 (2016), 1-18

(with E.R. van Dam and M.A. Fiol)

**6. Godsil-McKay switching and isomorphism** (journal), *Electron. J. Linear Algebra* 28 (2015), 4-11

(with A.E. Brouwer and W.H. Haemers)

**5. An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs** (journal), *Linear Algebra and Appl.* 34 (2014), 11-21

(with M.A. Fiol, W.H. Haemers and G. Perarnau)

**4. Algebraic Characterizations of Regularity Properties in Bipartite Graphs **(journal), *European J. Combin. *34(8) (2013), 1223-1231

(with C. Dalfó and M.A. Fiol)

**3. Cospectral graphs and regular orthogonal matrices of level 2** (journal), *Electron. J. Comb.* 19(3) (2012)

(with W.H. Haemers)

**2. Electron spin resonance study of single-walled carbon nanotubes** (journal), *Physica status solidi (b)* 248 (2011), 2564-2567

(with N. Ferrer-Anglada, V. Lloveras, J. Vidal-Gancedo and S. Roth)

**1. Electron spin resonance on single-walled carbon nanotubes obtained from different sources** (journal), *Physica status solidi (b) *247 (2010), 2823-2826

(with N. Ferrer-Anglada and S. Roth)

### Education

PhD in Mathematics from Tilburg University, The Netherlands (2015). Supervisors: Willem Haemers, Edwin van Dam. Get a copy of my PhD thesis, "Spectral Characterizations of Graphs", here.

MSc in Advanced Mathematics and Mathematical Engineering from the Polytechnic University of Catalonia, Spain (2011). Supervisor: Miquel Àngel Fiol. Get a copy of my MSc thesis, "Some Applications of Linear Algebra in Spectral Graph Theory", here.

BSc in Telecommunication Engineering from the Polytechnic University of Catalonia, Spain (2009).

### Talks

Schloos Dagstuhl: Logic and Random Discrete Structures, 6-11 February 2022, Germany

AIM Virtual Workshop Graph and Hypergraph Spectral Theory, 6-11 December 2021, US

5th Workshop Algebraic Graph Theory and its Applications, 1-5 November 2021, Russia

MAPTHE (Matrix Analysis and Potential Theory) workshop, 26-30 July 2021, Vallclara, Spain

AIM Online Research Community: inverse eigenvalue problem for graphs, June 2021, US

International workshop on Spectral Graph Theory, 29 May 2021, China

SIAM Conference on Applied Linear Algebra, 17-21 May 2021, New Orleans, US

International Day of Mathematics, 15 March 2021, The Netherlands

4st Workshop Algebraic Graph Theory and its Applications, 1-7 March 2021, Russia

Quantum Software Research Center (QuSoft) CWI seminar, 15 January 2021, Amsterdam, The Netherlands

3rd Workshop Algebraic Graph Theory and its Applications, 2-8 November 2020, Novosibirsk, Russia

Treewidth and Combinatorial Optimization workshop - TACO day, 19 October 2020, Maastricht, The Netherlands (POSTPONED)

23rd Conference of the International Linear Algebra Society, 22-26 June 2020, Galway, Ireland (POSTPONED)

Analytical and combintorial methods in quantum information, 9-13 September 2019, Edinburgh, Scotland

22nd Conference of the International Linear Algebra Society, 8-12 July 2019, Rio de Janeiro, Brazil

Bled '19 Slovenian International Conference in Graph Theory, 23-29 June 2019, Bled, Slovenia

Summer school on finite geometry&friends, 17-21 June 2019, Brussels, Belgium

Congreso Bienal de la Real Sociedad Matemática Española, 4-8 February 2019, Santander, Spain

Ghent PhD Seminar Mathematics, 13 December 2018, Ghent, Belgium

Diamant symposium, 29-30 November 2018, Veenendaal, The Netherlands

Monthly Operations Research seminar at Maastricht University, The Netherlands

### Misc

Dutch Combinatorics Network (DCN)