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Some Turรกn-type results for the signless Laplacian spectral radius
European journal of combinatorics (Print)Half a century ago, Bollob\'{a}s and Erd\H{o}s [Bull. London Math. Soc. 5 (1973)] proved that every $n$-vertex graph $G$ with $e(G)\ge (1- \frac{1}{k} + \varepsilon )\frac{n^2}{2}$ edges contains a blowup $K_{k+1}[t]$ with $t=\Omega_{k,\varepsilon}(\log ...
Jian Zheng, Yongtao Li, Yi-zheng Fan
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Signless Laplacian spectral conditions for even factors in graphs
Discrete Applied MathematicsA spanning subgraph $F$ of a graph $G$ is defined as an even factor of $G$, if the degree $d_F(v)=2k, k\in\mathbb{N}^+$ for every vertex $v\in V(G)$. This note establishes a sufficient condition to ensure that a connected graph $G$ of even order with the
Lu Li, Hechao Liu, Hongbo Hua, Zenan Du
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Signless Laplacians of finite graphs
The 2010 International Conference on Apperceiving Computing and Intelligence Analysis Proceeding, 2010We survey properties of spectra of signless Laplacain of graphs and discuss possibilities based on this matrix. In this paper, the eigen-value condition of Q(G), bounder of multiplicities of eigen-values, and several signless Laplacain eigenvector principles under some conditions, which are our results.
Bao Jiao, Yang Chun, Tianyong Qiang
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Linear and multilinear algebra
Let G be a multidigraph without self-loops. The complex Laplacian matrix of G, denoted by $ {L_{\mathbb {C}}}(G) $ LC(G), is defined in Barik et al. [On singularity and properties of eigenvectors of complex Laplacian matrix of multidigraphs.
S. Barik, Sane Umesh Reddy
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Let G be a multidigraph without self-loops. The complex Laplacian matrix of G, denoted by $ {L_{\mathbb {C}}}(G) $ LC(G), is defined in Barik et al. [On singularity and properties of eigenvectors of complex Laplacian matrix of multidigraphs.
S. Barik, Sane Umesh Reddy
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Extremal graphs for the sum of the first two largest signless Laplacian eigenvalues
Discrete Applied MathematicsFor a graph $G$, let $S_2(G)$ be the sum of the first two largest signless Laplacian eigenvalues of $G$, and $f(G)=e(G)+3-S_2(G)$. Very recently, Zhou, He and Shan proved that $K^+_{1,n-1}$ (the star graph with an additional edge) is the unique graph ...
Zi-Ming Zhou, Zhibin Du, Chang-Xiang He
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Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring โค๐
Georgian Mathematical Journal, 2023Let ๐ be a commutative ring with identity 1 โ 0 1\neq 0 and let Z โข ( R ) โฒ Z(R)^{\prime} be the set of all non-zero and non-unit elements of ring ๐ . Further, ฮ โฒ โข ( R ) \Gamma^{\prime}(R) denotes the cozero-divisor graph of ๐ , is an undirected graph ...
Mohd Rashid, M. Mozumder, Mohd Anwar
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Matrix-Tree Theorem of digraphs via signless Laplacians
Linear Algebra and its Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shu Li +3 more
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Discrete Mathematics, Algorithms and Applications, 2018
The distance signless Laplacian spectral radius of a connected graph [Formula: see text] is the largest eigenvalue of the distance signless Laplacian matrix of [Formula: see text], defined as [Formula: see text], where [Formula: see text] is the distance matrix of [Formula: see text] and [Formula: see text] is the diagonal matrix of vertex ...
Alhevaz, Abdollah +2 more
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The distance signless Laplacian spectral radius of a connected graph [Formula: see text] is the largest eigenvalue of the distance signless Laplacian matrix of [Formula: see text], defined as [Formula: see text], where [Formula: see text] is the distance matrix of [Formula: see text] and [Formula: see text] is the diagonal matrix of vertex ...
Alhevaz, Abdollah +2 more
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Laplacian and signless Laplacian Z-eigenvalues of uniform hypergraphs
Frontiers of Mathematics in China, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bu, Changjiang, Fan, Yamin, Zhou, Jiang
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, 2020
Many problems in real world, either natural or man-made, can be usefully represented by graphs or networks. Along with a complex topological structure, the weight is a vital factor in characterizing some properties of real networks.
Jia-bao Liu, J. Zhao, Zheng-Qun Cai
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Many problems in real world, either natural or man-made, can be usefully represented by graphs or networks. Along with a complex topological structure, the weight is a vital factor in characterizing some properties of real networks.
Jia-bao Liu, J. Zhao, Zheng-Qun Cai
semanticscholar +1 more source