Results 11 to 20 of about 2,218,762 (336)
On the spectral radius and energy of signless Laplacian matrix of digraphs. [PDF]
Heliyon, 2022 Let D be a digraph of order n and with a arcs. The signless Laplacian matrix Q ( D ) of D is defined as Q ( D ) = D e g ( D ) + A ( D ) , where A ( D ) is the adjacency matrix and D e g ( D ) is the diagonal matrix of vertex out-degrees of D. Among the eigenvalues of Q ( D ) the eigenvalue with largest modulus is the signless Laplacian spectral radius ...
Ganie HA, Shang Y.
europepmc +5 more sources
The bipartite Laplacian matrix of a nonsingular tree
Special Matrices, 2023 For a bipartite graph, the complete adjacency matrix is not necessary to display its adjacency information. In 1985, Godsil used a smaller size matrix to represent this, known as the bipartite adjacency matrix.
Bapat Ravindra B. +2 more
doaj +2 more sources
Spectral properties of the Laplacian and random matrix theories [PDF]
Journal de Physique Lettres, 1984 We investigate the fluctuation properties of the eigenvalues of the Laplacian in two dimensions with Dirichlet boundary conditions on a stadium. They are found to be consistent with the fluctuations of eigenvalues of random matrices (GOE). It is conjectured that this is true for any boundary such that the motion of a free particle elastically reflected
O. Bohigas, M.J. Giannoni, C. Schmit
openalex +5 more sources
Approximations of the Generalized Inverse of the Graph Laplacian Matrix [PDF]
Internet Mathematics, 2012 We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which is resource-demanding in terms of consumed time and memory and hence impractical whenever the graph is relatively
BOZZO, Enrico, FRANCESCHET, Massimo
openaire +5 more sources
The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs
Theory and Applications of Graphs, 2023 The α-Hermitian adjacency matrix Hα of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α.
Omar Alomari +2 more
doaj +3 more sources
The third smallest eigenvalue of the Laplacian matrix [PDF]
The Electronic Journal of Linear Algebra, 2001 Let G be a connected simple graph. The relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored. For a tree the complete description of the eigenvector corresponding to this eigenvalue is given and some results about the multiplicity of this eigenvalue are given. 1. Laplacian matrices.
Sukanta Pati
openalex +4 more sources
Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit [PDF]
, 2014 The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finitenumber $N$ of identical particles is introduced. We suggest a "fractional elastic harmonic potential", and obtain the $N$-periodic fractionalLaplacian
Collet, Bernard +3 more
core +2 more sources
The spectrum of the Laplacian matrix of a balanced binary tree
Linear Algebra and its Applications, 2002 AbstractLet L(Bk) be the Laplacian matrix of an unweighted balanced binary tree Bk of k levels. We prove that spectrum of L(Bk) isσL(Bk)=⋃j=1k−1σ(Tj)∪σ(Sk),where, for 1⩽j⩽k−1,Tj is the j×j principal submatrix of the tridiagonal k×k matrix Sk,Sk=120⋯0232⋱⋮02⋱⋱0⋮⋱⋱320⋯022.We derive that the multiplicity of each eigenvalue of Tj,1⩽j⩽k−1, as an eigenvalue ...
Óscar Rojo
openalex +5 more sources
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 +2 more
openalex +5 more sources
Correction to: Robust joint clustering of multi-omics single-cell data via multi-modal high-order neighborhood Laplacian matrix optimization. [PDF]
Bioinformatics, 2023 europepmc +3 more sources