A5038481848- Graph theory and applications
- Advanced Graph Theory Research
- Complex Network Analysis Techniques
- Matrix Theory and Algorithms
- graph theory and CDMA systems
- Opinion Dynamics and Social Influence
- Limits and Structures in Graph Theory
- Complexity and Algorithms in Graphs
- Mental Health Research Topics
- Finite Group Theory Research
- Advanced Queuing Theory Analysis
- Numerical methods for differential equations
- Interconnection Networks and Systems
- Electromagnetic Scattering and Analysis
- Blockchain Technology Applications and Security
- Game Theory and Applications
- Spectral Theory in Mathematical Physics
- COVID-19 epidemiological studies
- Rings, Modules, and Algebras
- Scientific Research and Discoveries
- Graph Labeling and Dimension Problems
- History and advancements in chemistry
- Peer-to-Peer Network Technologies
- Blind Source Separation Techniques
University of Ontario Institute of Technology
2019-2024
Iowa State University
2019-2022
First Technical University
2019-2022
University of Manitoba
2015-2018
Northwestern University
2017
The ranking of nodes in a network according to their centrality or ``importance'' is classic problem that has attracted the interest different scientific communities last decades. COVID-19 pandemic recently rejuvenated this problem, as may be used decide who should tested, vaccinated, first, population asymptomatic individuals. In paper, we review methods for node and compare performance benchmark considers community-based structure society. outcome procedure then which individuals possibly...
Random walks on graphs are often used to analyse and predict epidemic spreads investigate possible control actions mitigate them. In this study, we first show that models based random with a single stochastic agent (such as Google’s popular PageRank) may provide poor description of certain features spread: most notably, spreading times. Then, discuss another Markov chain method does reflect the correct mean infection times for disease spread between individuals in network, determine...
A sign pattern $\mathcal{A}$ is a matrix with entries in $\{+,-,0\}$. This article introduces the allow sequence of distinct eigenvalues for an $n\times n$ $\mathcal{A}$, defined as $q_{\rm seq}(\mathcal{A})=\langle q_1,\ldots,q_n\rangle$, $q_k=1$ if there exists real exactly $k$ having and $q_k=0$ otherwise. For example, 0,\ldots,0,1\rangle$ equivalent to requiring all eigenvalues, while 1,0,\ldots,0\rangle$ digraph being acyclic. Relationships between composite cycles are explored identify...
In a graph theory setting, Kemeny’s constant is parameter which measures weighted average of the mean first passage times in random walk on vertices graph. one sense, measure how well ‘connected’. An explicit computation for this given graphs order n consisting two large cliques joined by an arbitrary number parallel paths equal length, as different length. each case, shown to be O(n3), largest possible vertices. The approach used based interesting techniques spectral and includes...
The cop throttling number $th_c(G)$ of a graph $G$ for the game Cops and Robbers is minimum $k + capt_k(G)$, where $k$ cops $capt_k(G)$ rounds needed to capture robber on over all possible games in which both players play optimally. In this paper, we construct family graphs having $th_c(G)= \Omega(n^{2/3})$, establish sublinear upper bound number, show that chordal $O(\sqrt{n})$. We also introduce product $th_c^{\times}(G)$ as parameter minimizes person-hours used by cops. This extends...
Abstract Kemeny's constant for a connected graph is the expected time random walk to reach randomly chosen vertex , regardless of choice initial vertex. We extend definition nonbacktracking walks and compare it simple walks. explore relationship between these two parameters several families graphs provide closed‐form expressions regular biregular graphs. In nearly all cases, variant yields smaller constant.
Given any graph <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the spread of </inline-formula> is maximum difference between two eigenvalues adjacency matrix </inline-formula>. In this paper, we resolve a pair 20-year-old conjectures Gregory, Hershkowitz, and Kirkland...
In a graph theory setting, Kemeny’s constant is parameter which measures weighted average of the mean first passage times in random walk on vertices graph. one sense, measure how well ‘connected’. An explicit computation for this given graphs order n consisting two large cliques joined by an arbitrary number parallel paths equal length, as different length. each case, shown to be O(n3), largest possible vertices. The approach used based interesting techniques spectral and includes...
Given a strongly connected directed graph D, let S_D denote the set of all stochastic matrices whose is spanning subgraph D. We consider problem completely describing stationary vectors irreducible members S_D. Results from area convex polytopes and an association each matrix with undirected bipartite are used to derive conditions which must be satisfied by positive probability vector x in order for it admissible as some x, that possess also characterised.
Kemeny's constant is an interesting and useful quantifier describing the global average behavior of a Markov chain. In this article, we examine sensitivity to perturbations in transition probabilities. That is, consider problem generating condition number for give indication size change its value relative perturbation. We provide structured determine some illuminating upper lower bounds which connect conditioning well-studied numbers stationary vector also investigate several infinite...
If the Laplacian matrix of a graph has full set orthogonal eigenvectors with entries $\pm1$, then formed by taking columns as is Hadamard and said to be diagonalizable.
 In this article, we prove that if $n=8k+4$ only possible diagonalizable graphs are $K_n$, $K_{n/2,n/2}$, $2K_{n/2}$, $nK_1$, develop computational method for determining all diagonalized given any order. Using these two tools, determine present up order 36. Note it not even known how many matrices there
Kemeny's constant measures how fast a random walker moves around in graph. Expressions for can be quite involved, and this reason, many lines of research focus on graphs with structure that makes them amenable to more in-depth study (for example, regular graphs, acyclic 1-connected graphs). In article, we walks threshold which are an interesting family properties make examining difficult; is, they usually not regular, acyclic, 1-connected. This article is showcase various techniques...
We consider the cop-throttling number of a graph $G$ for game Cops and Robbers, which is defined to be minimum $(k + \text{capt}_k(G))$, where $k$ cops $\text{capt}_k(G)$ rounds needed capture robber on over all possible games. provide some tools bounding number, including showing that positive semidefinite (PSD) throttling variant zero forcing throttling, an upper bound number. also characterize graphs having low investigate how large can given graph. trees, unicyclic graphs, incidence...
The cop throttling number $th_c(G)$ of a graph $G$ for the game Cops and Robbers is minimum $k + capt_k(G)$, where $k$ cops $capt_k(G)$ rounds needed to capture robber on over all possible games in which both players play optimally. In this paper, we construct family graphs having $th_c(G)= \Omega(n^{2/3})$, establish sublinear upper bound number, show that chordal $O(\sqrt{n})$. We also introduce product $th_c^{\times}(G)$ as parameter minimizes person-hours used by cops. This extends...
If the Laplacian matrix of a graph has full set orthogonal eigenvectors with entries $\pm1$, then formed by taking columns as is Hadamard and said to be diagonalizable. In this article, we prove that if $n=8k+4$ only possible diagonalizable graphs are $K_n$, $K_{n/2,n/2}$, $2K_{n/2}$, $nK_1$, develop an efficient computation for determining all diagonalized given any order. Using these two tools, determine present up order 36. Note it not even known how many matrices there