Results 71 to 80 of about 102,179 (232)
Laplacian energy of trees with at most 10 vertices
Indonesian Journal of Combinatorics, 2018 Let Tn be the set of all trees with n ≤ 10 vertices. We show that the Laplacian energy of any tree Tn is strictly between the Laplacian energy of the path Pn and the star Sn, partially proving the conjecture that this hold for any tree.
Masood Ur Rehman +2 more
doaj +1 more source
A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws
Advanced Intelligent Discovery, EarlyView.The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows +7 more
wiley +1 more source
Some improved bounds on two energy-like invariants of some derived graphs
Open Mathematics, 2019 Given a simple graph G, its Laplacian-energy-like invariant LEL(G) and incidence energy IE(G) are the sum of square root of its all Laplacian eigenvalues and signless Laplacian eigenvalues, respectively. This paper obtains some improved bounds on LEL and
Cui Shu-Yu, Tian Gui-Xian
doaj +1 more source
Harnessing Digital Microstructure for Simulation‐Guided Optimization of Permanent Magnets
Advanced Intelligent Discovery, EarlyView.An experimental‐to‐computational workflow is presented that transforms experimental 3D focused ion beam‐scanning electron microscopy data into a simulation‐ready digital microstructure for multiphase functional materials. Using heavy‐rare‐earth‐free Nd–Fe–B magnets as a model system, the approach quantifies grain connectivity across complex secondary ...
Nikita Kulesh +4 more
wiley +1 more source
Advanced Intelligent Systems, EarlyView.This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley +1 more source
Certain Notions of Energy in Single-Valued Neutrosophic Graphs
Axioms, 2018 A single-valued neutrosophic set is an instance of a neutrosophic set, which provides us an additional possibility to represent uncertainty, imprecise, incomplete and inconsistent information existing in real situations.
Sumera Naz +2 more
doaj +1 more source
Total π-electron energy and Laplacian energy: How far the analogy goes? [PDF]
Journal of the Serbian Chemical Society, 2007 The Laplacian energy LE is a newly introduced molecular-graph-based analog of the total π-electron energy E. It is shown that LE and E have a similar structure-dependency only when molecules of different sizes are compared, when a good linear correlation
Radenković Slavko, Gutman Ivan
doaj +1 more source
Laplacian energies of vertices
Linear Algebra and its ApplicationsIn this work, we define the Laplacian and Normalized Laplacian energies of vertices in a graph, we derive some of its properties and relate them to combinatorial, spectral and geometric quantities of the graph.
openaire +3 more sources
Isolation and Reactivity of a Square‐Planar Trisamido Silane
Angewandte Chemie International Edition, EarlyView.We report the synthesis and comprehensive characterisation of a square‐planar Si(+IV) hydride supported by an unsymmetric, trianionic and dearomatised N,N,N‐pincer ligand. This system enables element–ligand cooperative reactivity as an alternative to silicon‐centred redox chemistry, illuminating a largely unexplored regime in high‐valent silicon ...
David M. J. Krengel +5 more
wiley +1 more source
On Relation between the Kirchhoff Index and Laplacian-Energy-Like Invariant of Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-11/μi and LEL(G)=Σi=1n-1
Emina Milovanovic +2 more
doaj +1 more source