9 papers
The forbidden structure for zero forcing number
Carlos A. Alfaro, Michael D. Barrus, Sergio Gerardo Gómez-Galicia +5
The {\it zero forcing number} of a graph , , is a well-studied parameter which arises from a color changing process and has strong connections to {\it minimum rank}, {\it…
The Smith normal form of Laplacian matrices of simplicial annuli and high dimensional trees
Carlos A. Alfaro, Jesús Uriel Medrano, Juan Pablo Serrano +2
Inspired by the generalization of the formula of determinant of the distance matrix of trees to -trees, we study the Smith normal form of Laplacian matrices associated with some…
Skirting the -tuples
Sam Adriaensen, Ferdinand Ihringer, William J. Martin +1
Let and be given. The set is a metric space of diameter under the Hamming metric . We seek a smallest set t…
The characterization of graphs with two trivial distance ideals
Carlos A. Alfaro, Teresa I. Hoekstra-Mendoza, Juan Pablo Serrano +1
The distance ideals of graphs are algebraic invariants that generalize the Smith normal form (SNF) and the spectrum of several distance matrices associated with a graph. In general…
Distance ideals of digraphs
Carlos A. Alfaro, Teresa I. Hoekstra-Mendoza, Juan Pablo Serrano +1
We focus on strongly connected, strong for short, digraphs since in this setting distance is defined for every pair of vertices. Distance ideals generalize the spectrum and Smith n…
Evolutive sandpiles
Carlos A. Alfaro, Juan Pablo Serrano, Ralihe R. Villagrán
The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple…