Results 61 to 70 of about 1,624,240 (288)

The sum of the largest and smallest signless laplacian eigenvalues and some Hamiltonian properties of graphs

Communications in Advanced Mathematical Sciences, 2018
The signless Laplacian eigenvalues of a graph $G$ are eigenvalues of the matrix $Q(G) = D(G) + A(G)$, where $D(G)$ is the diagonal matrix of the degrees of the vertices in $G$ and $A(G)$ is the adjacency matrix of $G$.
Rao Li
doaj   +1 more source

The Adjacency Matrix and the Discrete Laplacian Acting on Forms [PDF]

Mathematical Physics, Analysis and Geometry, 2019
We study the relationship between the adjacency matrix and the discrete Laplacian acting on 1-forms. We also prove that if the adjacency matrix is bounded from below it is not necessarily essentially self-adjoint. We discuss the question of essential self-adjointness and the notion of completeness.
Hatem Baloudi, Sylvain Golénia, Aref Jeribi   +2 more
openaire   +3 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

The spectra of the adjacency matrix and Laplacian matrix for some balanced trees

Linear Algebra and its Applications, 2005
The authors express the spectra of the adjacency and the Laplacian matrices of an unweighted rooted tree of \(k\) levels, such that in each level the vertices have the same degree, in terms of the spectra of a set of symmetric tridiagonal matrices.
Rojo, O, Soto, R
openaire   +4 more sources

Composition‐Aware Cross‐Sectional Integration for Spatial Transcriptomics

Advanced Intelligent Discovery, EarlyView.
Multi‐section spatial transcriptomics demands coherent cell‐type deconvolution, domain detection, and batch correction, yet existing pipelines treat these tasks separately. FUSION unifies them within a composition‐aware latent framework, modeling reads as cell‐type–specific topics and clustering in embedding space.
Qishi Dong, Zijian Huang, Xuanwu Wang, Zhenghui Feng, Wei Liu, Bingding Huang   +5 more
wiley   +1 more source

A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
In this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy ...
Şerife Büyükköse, Nurşah Mutlu Varlıoğlu   +1 more
doaj   +1 more source

Network Coherence in a Family of Book Graphs

Frontiers in Physics, 2020
In this paper, we study network coherence characterizing the consensus behaviors with additive noise in a family of book graphs. It is shown that the network coherence is determined by the eigenvalues of the Laplacian matrix.
Jing Chen, Yifan Li, Weigang Sun
doaj   +1 more source

From Data to Discovery: Machine Learning–Enabled Intelligent Characterization of Two‐Dimensional Materials

Advanced Intelligent Discovery, EarlyView.
Machine learning serves as a central engine for the intelligent characterization of two‐dimensional materials by integrating multimodal techniques, including optical microscopy, spectroscopy, electron microscopy, and scanning probe microscopy (SPM). This unified framework enables automated, high‐throughput, and quantitative extraction of structural ...
Zhi‐Long Cao, Jia‐Xu Yan
wiley   +1 more source

Moment-Based Spectral Analysis of Large-Scale Generalized Random Graphs

IEEE Access, 2017
This paper investigates the spectra of the adjacency matrix and Laplacian matrix for an artificial complex network model-the generalized random graph. We deduce explicit expressions for the first four asymptotic spectral moments of the adjacency matrix ...
Qun Liu, Zhishan Dong, En Wang
doaj   +1 more source

Maximizing the smallest eigenvalue of grounded Laplacian matrix

Journal of Global Optimization
For a connected graph $\mathcal{G}=(V,E)$ with $n$ nodes, $m$ edges, and Laplacian matrix $\boldsymbol{\mathit{L}}$, a grounded Laplacian matrix $\boldsymbol{\mathit{L}}(S)$ of $\mathcal{G}$ is a $(n-k) \times (n-k)$ principal submatrix of $\boldsymbol{\mathit{L}}$, obtained from $\boldsymbol{\mathit{L}}$ by deleting $k$ rows and columns corresponding ...
Xiaotian Zhou, Run Wang, Wei Li 0055, Zhongzhi Zhang   +3 more
openaire   +4 more sources