A5037777428- Graph theory and applications
- Algebraic and Geometric Analysis
- Advanced Graph Theory Research
- Finite Group Theory Research
- Advanced Combinatorial Mathematics
- Advanced Topics in Algebra
- Matrix Theory and Algorithms
- Interconnection Networks and Systems
- Topological and Geometric Data Analysis
- Quantum Computing Algorithms and Architecture
- Quantum Mechanics and Applications
- DNA and Biological Computing
- Random Matrices and Applications
- Spectral Theory in Mathematical Physics
- Mobile Ad Hoc Networks
- Formal Methods in Verification
- Graph Labeling and Dimension Problems
- Graph Theory and Algorithms
- Geometric and Algebraic Topology
- Computability, Logic, AI Algorithms
- Advanced Algebra and Geometry
- Mathematical Analysis and Transform Methods
- Algebraic structures and combinatorial models
- Complexity and Algorithms in Graphs
- Energy Efficient Wireless Sensor Networks
Southern Illinois University Edwardsville
2013-2024
Laboratoire Lorrain de Recherche en Informatique et ses Applications
2010
Université de Lorraine
2010
Given a finite simple graph $G$ on $m$ vertices, the zeon combinatorial Laplacian $\Lambda$ of is an $m\times m$ having entries in complex algebra $\mathbb{C}\mathfrak{Z}$. It shown here that if has unique vertex $v$ degree $k$, then eigenvalue $\lambda$ whose scalar part $k$. Moreover, canonical expansion nilpotent (dual) counts cycles based at $G$. With appropriate generalization $G$, all are counted by $\Lambda$. Moreover when generalized can be viewed as self-adjoint operator...
One of the greatest challenges in computing and estimating important node metrics a structural graph is centrality. Since centrality an essential concept social network analysis (SNA), it used to define importance like wireless sensor (WSN). Route optimization another feature network. This paper proposes alternative solution route problems by using multi-constrained optimal path (MCOP) approach. A new metric called operator calculus (POC) proposed as way determine nodes with high deployment....
Wireless sensor networks (WSN) are inherently multi - constrained. They need to preserve energy while offering reliable and timely data reporting for a non-negligible number of scenarios. This is particularly true when node should decide which forwarder has be chosen routing packet. Nevertheless, solving multi-constrained problems NP-complete. Most approaches involve transforming the problem into single constrained using cost function, although this may lead suboptimal solutions. Some other...
An innovative minimal paths algorithm based on operator calculus in graded semigroup algebras is described. Classical approaches to routing problems invariably require construction of trees and the use heuristics prevent combinatorial explosion. The approach presented herein, however, allows such explicit tree constructions be avoided. Moreover, implicit structures underlying problem are pruned automatically by inherent properties used this approach. proposed here applied precomputed a...
Combinatorial Algebras and Their Properties Combinatorics Graph Theory Operator Calculus Probability on Algebraic Structures Computational Complexity Symbolic Computations Using Mathematica.
While a number of researchers have previously investigated the relationship between graph theory and quantum probability, current work explores new perspective. The approach this paper is to begin with an arbitrary having no established probability use that construct space in which moments random variables reveal information about graph's structure. Given finite odd integer m ⩾ 3, fermion annihilation operators are used family whose mth correspond m-cycles. then generalized recover m-cycles...
Central to the theory of free probability is notion summing multiplicative functionals on lattice non-crossing partitions.In this paper, a graph-theoretic perspective partitions investigated in which independent sets graphs correspond partitions.By associating particular with elements "zeon" algebras (commutative subalgebras fermion algebras), functions can be summed over segments lattices by employing methods "zeon-Berezin" operator calculus.In particular, properties algebra are used "sieve...
In recent work, the authors used canonical lowering and raising operators to define Appell systems on Clifford algebras of arbitrary signature.Appell can be interpreted as polynomial solutions generalized heat equations, in probability theory they have been obtain non-central limit theorems.The natural grade-decomposition a algebra signature lends it system decomposition.In current defined are chains cochains vector spaces underlying algebra, compute associated homology cohomology groups,...