37 citations · 69 across the 13 of their papers we have counts for
4 papers · 1 filter
Critical ideals, minimum rank and zero forcing number
Carlos A. Alfaro, Jephian C. -H. Lin
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is…
On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed
Carlos A. Alfaro, Adrián Vázquez-Ávila
A linear system is a pair where is a family of subsets on a ground finite set such that , for every $l,l^\prime \in \mat…
Distance ideals of graphs
Carlos A. Alfaro, Libby Taylor
We introduce the concept of distance ideals of graphs, which can be regarded as a generalization of the Smith normal form and the spectra of the distance matrix of a graph. We obta…
Digraphs with at most one trivial critical ideal
Carlos A. Alfaro, Carlos E. Valencia, Adrián Vázquez-Ávila
Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterizatio…