12 citations · 40 across the 78 of their papers we have counts for
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The inverse nullity pair problem and the strong nullity interlacing property
Aida Abiad, Bryan A. Curtis, Mary Flagg +3
The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph . In…
Descriptive complexity of controllable graphs
Aida Abiad, Anuj Dawar, Octavio Zapata
Let be a graph on vertices with adjacency matrix , and let be the all-ones vector. We call controllable if the set of vectors $\mathbf{1}, A\mathbf{1},…
On the existence of small strictly Neumaier graphs
Aida Abiad, Maarten De Boeck, Sjanne Zeijlemaker
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this work, we prove several results on the existence of small strictly Neumaier graphs. In par…
Eigenvalue Bounds for Sum-Rank-Metric Codes
Aida Abiad, Antonina P. Khramova, Alberto Ravagnani
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric codes, with focus on their dimension and block length. The sum-rank metric is a combination of…
Cospectral mates for generalized Johnson and Grassmann graphs
Aida Abiad, Jozefien D'haeseleer, Willem H. Haemers +1
We provide three infinite families of graphs in the Johnson and Grassmann schemes that are not uniquely determined by their spectrum. We do so by constructing graphs that are cospe…
The Diameter of Sum Basic Equilibria Games
Aida Abiad, Carme Alvarez, Arnau Messegué
A graph of order is said to be a sum basic equilibrium if and only if for every edge from and any node from , when performing the swap of the edge for…
Distinguishing graphs by their spectra, Smith normal forms and complements
Aida Abiad, Carlos A. Alfaro, Ralihe R. Villagrán
The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose compleme…
A switching method for constructing cospectral gain graphs
Aida Abiad, Francesco Belardo, Antonina P. Khramova
A gain graph over a group , also referred to as -gain graph, is a graph where an element of a group , called gain, is assigned to each oriented edge, in such a way that th…
Positive and Negative Square Energies of Graphs
Aida Abiad, Leonardo de Lima, Dheer Noal Desai +3
The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of . Let denote the sum of the squares of the positive an…
Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
Aida Abiad, Shaun M. Fallat, Mark Kempton +5
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the j…
On the diameter and zero forcing number of some graph classes in the Johnson, Grassmann and Hamming association scheme
Aida Abiad, Robin Simoens, Sjanne Zeijlemaker
We determine the diameter of generalized Grassmann graphs and the zero forcing number of some generalized Johnson graphs, generalized Grassmann graphs and the Hamming graphs. Our w…