Permanent of the Laplacian matrix of trees and bipartite graphs
Discrete Mathematics, 1984 Let \(G=(V,E)\) be a graph without loops and multiple edges with vertex set \(V=\{v_ 1,...,v_ n\}\) and edge set E. Suppose the degree of vertex \(v_ i\) equals \(d_ i\) for \(i=1,...,n\) and let \(D=D(G)\) be the diagonal matrix whose (i,i)-entry is \(d_ i\).
Richard A. Brualdi, John L. Goldwasser
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Robust joint clustering of multi-omics single-cell data via multi-modal high-order neighborhood Laplacian matrix optimization. [PDF]
Bioinformatics, 2023 Jiang H, Zhan S, Ching WK, Chen L.
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JLMC: A clustering method based on Jordan-Form of Laplacian-Matrix
, 2014 Among the current clustering algorithms of complex networks, Laplacian-based spectral clustering algorithms have the advantage of rigorous mathematical basis and high accuracy.
J Niu (13383387) +2 more
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Journal of Medical Radiation Sciences, Volume 72, Issue 1, Page 93-105, March 2025.This study developed a two‐stage model using radiomics‐based multiparametric MRI and clinical indicators to help identify and grade clinically significant prostate cancer. The model showed promising levels of diagnostic accuracy and predictive performance.
Yuyan Zou +10 more
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Graph Convolutional Network Using Adaptive Neighborhood Laplacian Matrix for Hyperspectral Images with Application to Rice Seed Image Classification. [PDF]
Sensors (Basel), 2023 Orozco J +4 more
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The Laplacian matrix of a graph [PDF]
, 1995 This paper is a study of the various matrices associated with graphs. In Chapter 1, the relationship between the Laplacian matrix and the Incidence matrix is explored. The Matrix-Tree Theorem (MTT) is stated here. One of the main objectives of this paper
Amar, Alka
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Distance matrix and Laplacian of a tree with attached graphs [PDF]
, 2004 A tree with attached graphs is a tree, together with graphs defined on its partite sets. We introduce the notion of incidence matrix, Laplacian and distance matrix for a tree with attached graphs.
R.B. Bapat, Bapat, R. B., Bapat, R.B.
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Kernel Bounds for Parabolic Operators Having First‐Order Degeneracy at the Boundary
Mathematische Nachrichten, EarlyView.ABSTRACT We study kernel estimates for parabolic problems governed by singular elliptic operators ∑i,j=1N+1qijDij+cDyy,cγ+1>0,γ=qN+1,N+1,$$\begin{equation*} \sum _{i,j=1}^{N+1}q_{ij}D_{ij}+c\frac{D_y}{y},\qquad \frac{c}{\gamma }+1>0, \quad \gamma =q_{N+1,N+1}, \end{equation*}$$in the half‐space R+N+1={(x,y):x∈RN,y>0}$\mathbb {R}^{N+1}_+=\lbrace (x,y ...
L. Negro, C. Spina
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Sharp decrease in the Laplacian matrix rank of phase-space graphs: a potential biomarker in epilepsy. [PDF]
Cogn Neurodyn, 2021 Yang Z, Fan D, Wang Q, Luan G.
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On some properties of the Laplacian matrix revealed by the RCM algorithm [PDF]
, 2016 summary:In this paper we present some theoretical results about the irreducibility of the Laplacian matrix ordered by the Reverse Cuthill-McKee (RCM) algorithm. We consider undirected graphs with no loops consisting of some connected components. RCM is a
Palomares Chust, Alberto +7 more
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