12 citations · 40 across the 78 of their papers we have counts for
20 papers · 1 filter
The Zero Forcing Number of Graph Powers
Aida Abiad, Mary Flagg, Sina Ghasemi Nezhad +1
The -th power of a simple graph , denoted , is the graph with vertex set where two vertices are adjacent if they are within distance in . We investigate th…
A unified framework for existing and new constructions of Neumaier graphs
Aida Abiad, Wouter Castryck, Maarten De Boeck +2
A Neumaier graph is a non-complete edge-regular graph containing a regular clique; it is called strictly Neumaier if it is not strongly regular. In this paper we present a construc…
Switching graphs and designs
Aida Abiad, Dean Crnković, Louka Peters +1
Switching methods can be seen as certain local transformations that do not alter their basic parameters of a combinatorial structure. Efforts have been devoted in the literature to…
Kemeny's constant via matrix compression and eigenvalue interlacing
A. Abiad, Á. Carmona, A. M. Encinas +3
Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, capturing global properties of a Markov chain. We develop a matrix-analytic fram…
Fort Abundance in Zero Forcing
Aida Abiad, Sina Ghasemi Nezhad
This paper paper concerns the study of forts, the sets that obstruct zero forcing. We show that every block graph on vertices has at least minimal forts, extending a rece…
Localization of the Caro-Wei bound and its applications to bipartiteness
Aida Abiad, Hitesh Kumar, Shivaramakrishna Pragada
We confirm a conjecture of Brause, Randerath, Rautenbach and Schiermeyer (2016) by proving a localized lower bound on the independence number of a graph that strengthens the classi…
Spectral and Additive Combinatorial Methods for Cycles and Absorbing Sets in Lifted-Product Quantum LDPC Codes
Aida Abiad, Nichola Castriota
The finite-length performance of quantum low-density parity-check (LDPC) codes under iterative decoding is governed by small substructures of the Tanner graph, principally short cy…
Spectral Sparsification of Laplacian-Constrained Gaussian and Hüsler-Reiss Graphical Models
Ignacio Echave-Sustaeta Rodríguez, Aida Abiad, Frank Röttger
Graph Laplacians encode graph structures in matrix form, and thus facilitate the application of linear algebra to graph theory. In statistics, two related families of probabilistic…
Wang-Qiu-Hu switching and isomorphism
Aida Abiad, Hong-Jun Ge
Cospectral graphs (graphs that share the same eigenvalues) expose the limitations of using the graph spectrum to uniquely identify graphs, and they also help to understand what str…
Spectral bounds for distance coloring and packing parameters of graphs via semidefinite programming
Aida Abiad, Yue Yang, Jiang Zhou
Using methods from spectral graph theory and semidefinite programming, we obtain sharp spectral bounds for several graph parameters related to distance colorings and packing, inclu…
Learning Gaussian Graphical Models under Total Positivity via Spectral Graph Sparsification
Ignacio Echave-Sustaeta Rodríguez, Aida Abiad, Frank Röttger
Many practical data analysis tasks reduce to learning, from observed samples, how a collection of variables depend on each other. A widely used approach is to fit a Gaussian graphi…
An algebraic-combinatorial framework for finding the average hitting times in graphs with high regularity
Aida Abiad, Yusaku Nishimura
For any given vertices and in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex starting at…
Optimization and complexity of inertia-type bounds on the independence and chromatic numbers of graph powers
Aida Abiad, Stan van Hoesel, Valentin Michaux
The inertia bound, introduced by Cvetković in 1971, is a fundamental result in spectral graph theory that provides an upper bound for the independence number of a graph in terms of…
Semidefinite and linear programming bounds for sum-rank-metric codes and non-existence results
Aida Abiad, Antonina P. Khramova, Sven C. Polak +1
The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distrib…
A general switching method for constructing E-cospectral hypergraphs
Aida Abiad, Joshua Cooper, Utku Okur
Spectral hypergraph theory studies the structural properties of a hypergraph that can be inferred from the eigenvalues and the eigenvectors of either matrices or tensors associated…
Computing fixed point free automorphisms of graphs
Aida Abiad, Gabriel Coutinho, Emanuel Juliano +2
In 1981, Lubiw proved that the fixed point free automorphism problem (FPFAut) is NP-complete: given a graph G, determine whether there exists an automorphism that maps no vertex of…
Logical aspects of isomorphism of controllable graphs and cospectrality of distance-regularized graphs
Aida Abiad, Anuj Dawar, Octavio B. Zapata-Fonseca
We consider isomorphism of controllable graphs and cospectrality of distance-regularized graphs (which are known to be distance-regular or distance-biregular) in relation to logica…
A strong nullity parameter for rooted graphs
Aida Abiad, Mary Flagg, H. Tracy Hall +2
The inverse eigenvalue problem of a graph studies the possible spectra of matrices associated with , including as an important subproblem the possible nullities of such a ma…
Propagation processes on (hyper)graphs: where zero forcing and burning meet
Aida Abiad, Pax Mallee
The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this pap…
The edge-isoperimetric number of graphs and their powers
Aida Abiad, Nils van de Berg, Emanuel Juliano +4
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph p…