Results 31 to 40 of about 18,314 (299)
Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order [PDF]
, 2010 For every integer n≥4, it is proved that there is a unique graph of order n which maximizes the spectral radius of the unoriented Laplacian matrix over all bicyclic graphs of order n, namely, the graph obtained from the cycle C 4 by first adding a chord ...
Fan, Yi-zheng; 譚必信; Tam, Bit-shun; Zhou, Jun
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More on Spectral Analysis of Signed Networks
Complexity, 2018 Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity
Guihai Yu, Hui Qu
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Laplacian matrix and its applications [PDF]
, 2022 Grafy a Markovské řetězce je možné reprezentovat pomocí matic. Jednou z nejběžnějších forem reprezentace pro grafy je Laplaceova matice. Tato práce o ní dává ucelený přehled a nachází Laplaceova spektra několika základních typů grafů.
Daniel Khol
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Trees with matrix weights: Laplacian matrix and characteristic-like vertices
Linear Algebra and its Applications, 2022 It is known that there is an alternative characterization of characteristic vertices for trees with positive weights on their edges via Perron values and Perron branches. Moreover, the algebraic connectivity of a tree with positive edge weights can be expressed in terms of Perron value.
Swetha Ganesh, Sumit Mohanty
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On the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph [PDF]
, 2013 summary:The Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph are the characteristic polynomials of its Laplacian matrix, signless Laplacian matrix and normalized Laplacian matrix, respectively.
Li, Jianxi, Guo, Ji-Ming, Shiu, Wai Chee
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Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
Trends in Computational and Applied Mathematics, 2021 We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic.
R. O. Braga +2 more
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The Laplacian spread of graphs [PDF]
, 2009 summary:The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread,
Tan, Ying-Ying +4 more
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On distance Laplacian energy in terms of graph invariants [PDF]
, 2023 summary:For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $ \rho ^{L}_{1}\geq \rho ^{L}_{2}\geq \cdots \geq \rho ^{L}_{n}$, the distance Laplacian energy ${\rm DLE} (G)$ is defined as ${\rm DLE} (G)=\sum _{i=1}^{n}|\rho ^
Rather, Bilal A. +3 more
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Hermitian Laplacian Matrix of Directed Graphs [PDF]
Jisuanji kexue, 2023 Laplacian matrix plays an important role in the research of undirected graphs.From its spectrum,some structure and properties of a graph can be deduced.Based on this,several efficient algorithms have been designed for relevant tasks in graphs,such as ...
LIU Kaiwen, HUANG Zengfeng
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The p-spectral radius of the Laplacian matrix
Applicable Analysis and Discrete Mathematics, 2018 The p-spectral radius of a graph G=(V,E) with adjacency matrix A is defined as ?(p)(G) = max||x||p=1 xT Ax. This parameter shows connections with graph invariants, and has been used to generalize some extremal problems. In this work, we define the p-spectral radius of the Laplacian matrix L as ?(p)(G) = max||x||p=1 xT Lx.
Borba, Elizandro Max +3 more
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