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Indecomposable laplacian integral graphs
Linear Algebra and its Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grone, Robert, Merris, Russell
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Kernels of Directed Graph Laplacians [PDF]
The Electronic Journal of Combinatorics, 2006 Let $G$ denote a directed graph with adjacency matrix $Q$ and in-degree matrix $D$. We consider the Kirchhoff matrix $L=D-Q$, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when $G$ is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of $G$.
Caughman, John S., IV, Veerman, J. J. P.
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Learning graph Laplacian with MCP
Optimization Methods and Software, 2023 32 ...
Yangjing Zhang +2 more
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On net-Laplacian energy of signed graphs
Communications in Combinatorics and Optimization, 2017 A signed graph is a graph where the edges are assigned either positive or negative signs. Net degree of a signed graph is the difference between the number of positive and negative edges incident with a vertex. It is said to be net-regular if all its
Nutan G. Nayak
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A novel method to construct cospectral graphs based on RT operation [PDF]
AIP AdvancesThis paper presents a new graph operation, RT(G), which is formed by transforming each vertex and edge of the original graph G into a triangle. We analyze the relationship between the signless Laplacian characteristic polynomials of the graph RT(G) and ...
Xiu-Jian Wang +2 more
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Central vertex join and central edge join of two graphs
AIMS Mathematics, 2020 The central graph $C(G)$ of a graph $G$ is obtained by sub dividing each edge of $G$ exactly once and joining all the nonadjacent vertices in $G$. In this paper, we compute the adjacency, Laplacian and signless Laplacian spectra of central graph of a ...
Jahfar T K, Chithra A V
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Bounds for Laplacian graph eigenvalues [PDF]
Mathematical Inequalities & Applications, 2012 Let G be a connected simple graph whose Laplacian eigenvalues are 0 = μn (G) μn−1 (G) · · · μ1 (G) . In this paper, we establish some upper and lower bounds for the algebraic connectivity and the largest Laplacian eigenvalue of G . Mathematics subject classification (2010): 05C50, 15A18.
Maden, A. Dilek, Buyukkose, Serife
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The bounds of the energy and Laplacian energy of chain graphs
AIMS Mathematics, 2021 Let $G$ be a simple connected graph of order $n$ with $m$ edges. The energy $\varepsilon(G)$ of $G$ is the sum of the absolute values of all eigenvalues of the adjacency matrix $A$.
Yinzhen Mei, Chengxiao Guo, Mengtian Liu
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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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Tarantula graphs are determined by their Laplacian spectrum
Electronic Journal of Graph Theory and Applications, 2021 A graph G is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to G. A graph which is a collection of hexagons (lengths of these cycles can be different) all sharing precisely one vertex ...
Reza Sharafdini, Ali Zeydi Abdian
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