12 citations · 40 across the 78 of their papers we have counts for
13 papers · 1 filter
Tales of Hoffman: from a distance
Aida Abiad, Jan Meeus
Hoffman proved that a graph with adjacency eigenvalues and chromatic number satisfies where is the smallest integer such th…
The Shannon capacity of graph powers
Aida Abiad, Cristina Dalfó, Miquel Àngel Fiol
For a graph , its -th graph power is constructed by placing an edge between two vertices if they are within distance . We consider the problem of deriving upper boun…
Improved Gilbert-Varshamov bound for sum-rank-metric codes via graph theory
Aida Abiad, Harper Reijnders, Michael Tait
We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that…
On the Diameter of Arrangements of Topological Disks
Aida Abiad, Boris Aronov, Mark de Berg +3
Let be a set of topological disks in the plane and let be the arrangement induced by $\mathcal{D}…
The Eigenvalue Method in Coding Theory
Aida Abiad, Loes Peters, Alberto Ravagnani
We lay down the foundations of the Eigenvalue Method in coding theory. The method uses modern algebraic graph theory to derive upper bounds on the size of error-correcting codes fo…
A graph energy conjecture through the lenses of semidefinite programming
Aida Abiad, Gabriel Coutinho, Emanuel Juliano +1
Let be a graph on vertices with independence number . Let be the energy of a graph, defined as the sum of the absolute values of the adjacency eigenv…
On the -forcing number: computational approach and exact values
Aida Abiad, Maryam Moghaddas
Zero forcing is a graph coloring process that is used to model spreading phenomena in real-world scenarios. It can also be viewed as a single-player combinatorial game on a graph,…
Hoffman colorability of (strongly) regular graphs
Aida Abiad, Bart De Bruyn, Thijs van Veluw
Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining…
Infinitely many counterexamples to a conjecture of Lovász
Aida Abiad, Frederik Garbe, Xavier Povill +1
Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in -partite -uniform hypergraphs, Lovász formulated a stronger conjec…
Eigenvalue bounds for distance-edge colorings
Aida Abiad, Harper Reijnders
For a fixed positive integer , we consider the graph colouring problem in which edges at distance at most are given distinct colours. We obtain sharp lower bounds for the di…
A Spectral Approach to Kemeny's Constant
Aida Abiad, Ángeles Carmona, Andrés M. Encinas +2
Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, providing insight into the global behavior of a Markov chain. We present a novel…
Eigenvalue bounds for the quantum chromatic number of graph powers
Aida Abiad, Benjamin Jany
The quantum chromatic number, a generalization of the chromatic number, was first defined in relation to the non-local quantum coloring game. We generalize the former by defining t…
Counting cospectral graphs obtained via switching
Aida Abiad, Nils Van de Berg, Robin Simoens
Switching is an operation on a graph that does not change the spectrum of the adjacency matrix, thus producing cospectral graphs. An important activity in the field of spectral gra…