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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…
Generalized Token Graphs
C. Amairani Herrera-Ramirez, Teresa I. Hoekstra-Mendoza
In this paper we give a new generalization of token graphs. Given two integers and a graph we define the generalized token graph of the graph , to be the gr…
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…
Kernels in digraphs with colored vertices
Mucuy-kak Guevara, Teresa I. Hoekstra-Mendoza, Miguel Licona-Velazquez
In this paper, we introduce the concept of up-color kernel, which is a generalization of a kernel for vertex-colored digraphs. We give sufficient and necessary conditions for sever…
Bikernels by monochromatic paths
Dennis J. Diaz-Diaz, Isaías F. de-la-Fuente-Jimenez, Teresa I. Hoekstra-Mendoza +2
In this paper, we introduce the concept of bikernel by monochromatic paths of a bicolored digraph. This concept is strongly motivated by the existing notions of kernels, kernels by…
On the Automorphisms of Token Graphs Generated by -cuts with the Same Neighbours
Ruy Fabila-Monroy, Sergio Gerardo Gómez-Galicia, Daniel Gregorio-Longino +2
Let be a connected graph on vertices and an integer. The -token graph of is the graph whose vertices are all the -subsets of vertices o…
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…
The kernel-subdivision number of a digraph
Teresa I. Hoekstra-Mendoza, Miguel E. Licona-Velázquez, Rocío Rojas-Monroy
It is well known that determining if a digraph has a kernel is an NP-complete problem. However, Topp proved that when subdividing every arc of a digraph we obtain a digraph with a…
Recovering trees from the cohomology ring of their configuration spaces
Teresa I. Hoekstra-Mendoza
Given a tree , the cohomology ring of its unordered configuration space is an exterior face algebra if is a binary core tree (if by removing the…