A5083123899- Graph theory and applications
- graph theory and CDMA systems
- Advanced Graph Theory Research
- Limits and Structures in Graph Theory
- Computability, Logic, AI Algorithms
- Game Theory and Applications
- Mathematical Analysis and Transform Methods
- Mathematical Approximation and Integration
- Sparse and Compressive Sensing Techniques
- Finite Group Theory Research
- Graph Labeling and Dimension Problems
- Matrix Theory and Algorithms
- Quasicrystal Structures and Properties
- Advanced Algebra and Geometry
- advanced mathematical theories
- Advanced Optimization Algorithms Research
- Graph Theory and Algorithms
- Cellular Automata and Applications
- Stochastic processes and statistical mechanics
- Evolutionary Game Theory and Cooperation
- Experimental Behavioral Economics Studies
Hollins University
2022-2024
Iowa State University
2018-2020
Christopher Newport University
2019
Zero forcing is a coloring game played on graph where each vertex initially colored blue or white and the goal to color all vertices by repeated use of (deterministic) change rule starting with as few possible. Probabilistic zero yields discrete dynamical system governed Markov chain. Since in connected any one can eventually entire using probabilistic forcing, expected time do this studied. Given transition matrix for process, an exact formula established propagation time. chains are...
Abstract The maximum nullity of a simple graph G, denoted M(G), is the largest possible over all symmetric real matrices whose ijth entry nonzero exactly when fi, jg an edge in G for i =6 j, and iith any number. zero forcing number Z(G), minimum blue vertices needed to force by applying color change rule. This research motivated longstanding question characterizing graphs which M(G) = Z(G). following conjecture was proposed at 2017 AIM workshop Zero its applications: If bipartite 3-...
In this paper, we initiate the study of inverse eigenvalue problem for probe graphs. A graph is a whose vertices are partitioned into and non-probe such that form an independent set. general, used to represent set graphs can be obtained by adding edges between vertices. The considers family matrices zero-nonzero pattern defined asks which spectra achievable in family. We ask same question start establishing bounds on maximum nullity defining zero forcing number. Next, focus two parallel...
Zero forcing is a coloring game played on graph where each vertex initially colored blue or white and the goal to color all vertices by repeated use of (deterministic) change rule starting with as few possible. Probabilistic zero yields discrete dynamical system governed Markov chain. Since in connected any one can eventually entire using probabilistic forcing, expected time do this studied. Given transition matrix for process, we establish an exact formula propagation time. We apply chains...
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with inverse eigenvalue problem for graphs. More recently class graphs which all associated symmetric matrices possess (denoted $G^{SSP}$) were studied, and along these lines we aim to study properties that exhibit so-called barbell partition. Such partition is known impediment membership $G^{SSP}$. In particular consider existence partitions under various standard useful...
The Kaczmarz algorithm is an iterative method for solving a system of linear equations. It can be extended so as to reconstruct vector $x$ in (separable) Hilbert space from the inner-products $\{\langle x, \phi_{n} \rangle\}$. algorithms defines sequence approximations \rangle\}$; these only converge when $\{\phi_{n}\}$ ${effective}$. We dualize that obtained \rangle\}$ by using second $\{\psi_{n}\}$ reconstruction. This allows recovery even not effective; particular, our dualization yields...
Zero forcing is a process that colors the vertices of graph blue by starting with some and applying color change rule. Throttling minimizes sum number initial time to graph. In this paper, we study throttling for skew zero forcing. We characterize graphs order $n$ numbers $1, 2, n-1$, $n$. find exact paths, cycles, balanced spiders short legs. addition, sharp lower bound on in terms diameter.
If $S$ is a subset of an abelian group $G$, the polychromatic number in $G$ largest integer $k$ so that there $k-$coloring elements such every translate gets all colors. We determine sets size 2 or 3 integers mod n.
Motivated in part by an observation that the zero forcing number for complement of a tree on $n$ vertices is either $n-3$ or $n-1$ one exceptional case, we consider more general graphs under some conditions, particularly those do not contain complete bipartite subgraphs. We also move well beyond trees and completely study all possible numbers complements unicyclic cactus graphs.
SummaryIn this article, we examine a simplified version of the game Blokus. We count number completed boards in game, discussing how can be examined terms both combinatorics and graph theory, provide takeaways for undergraduate mathematics.