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Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph
TLDR
Two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities, and are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Expand
Zero forcing propagation time on oriented graphs
TLDR
The minimum number of iterations needed for this color change rule to color all of the vertices blue, also known as the propagation time, for oriented graphs is considered. Expand
Note on von Neumann and R\'enyi entropies of a Graph
We conjecture that all connected graphs of order $n$ have von Neumann entropy at least as great as the star $K_{1,n-1}$ and prove this for almost all graphs of order $n$. We show that connectedExpand
MINIMUM RANK OF GRAPHS WITH LOOPS
A loop graph $\mf G$ is a finite undirected graph that allows loops but does not allow multiple edges. The set $\sym(\lG)$ of real symmetric matrices associated with a loop graph $\lG$ of order $n$Expand
Persistent organic pollutants in tropical coastal and offshore environment: part A—atmospheric polycyclic aromatic hydrocarbons
Abstract Air samples were collected at four sites from August 2009 to May 2010. Temporal variation of polycyclic aromatic hydrocarbon (PAH) concentrations showed the highest concentration in NovemberExpand
Zero forcing number, Grundy domination number, and their variants
This paper presents strong connections between four variants of the zero forcing number and four variants of the Grundy domination number. These connections bridge the domination problem and theExpand
On the error of a priori sampling: zero forcing sets and propagation time
TLDR
A purely linear algebraic interpretation of zero forcing is given and the propagation time of a chosen set is given which is the number of steps the rule must be applied in order to color all the vertices of a graph. Expand
On the Distance Spectra of Graphs
The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distanceExpand
Critical ideals, minimum rank and zero forcing number
TLDR
This work studies the relation of the zero forcing number and minimum rank of a graph with a third one, the algebraic co-rank; that is defined as the largest $i$ such that thei-th critical ideal is trivial. Expand
The Inverse Eigenvalue Problem of a Graph, Zero Forcing, and Related Parameters
The authors of this piece are organizers of the AMS 2020 Mathematics Research Communities summer conference Finding Needles in Haystacks: Approaches to Inverse Problems Using Combinatorics and LinearExpand
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