Results 11 to 20 of about 1,304 (147)
Journal of Mathematics, 2021 Let G be a graph with n vertices, and let LG and QG denote the Laplacian matrix and signless Laplacian matrix, respectively. The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the permanent of the characteristic ...
Tingzeng Wu, Tian Zhou
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On graphs with adjacency and signless Laplacian matrices eigenvectors entries in {−1,+1} [PDF]
Linear Algebra and its Applications, 2021 Let $G$ be a simple graph. In 1986, Herbert Wilf asked what kind of graphs have an eigenvector with entries formed only by $\pm 1$? In this paper, we answer this question for the adjacency, Laplacian and signless Laplacian matrix of a graph. Besides, we generalize the concept of an exact graph to the adjacency and signless Laplacian matrices.
Jorge Alencar, Leonardo de Lima
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Dynamical systems on graphs through the signless Laplacian matrix [PDF]
Ricerche di Matematica, 2017 There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree characteristics, using the signless Laplacian matrix.
Giunti, B., Perri, V.
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The $γ$-Signless Laplacian Adjacency Matrix of Mixed Graphs [PDF]
, 2022 The $α$-Hermitian adjacency matrix $H_α$ 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 $α$. This enables us to define an incidence matrix of mixed graphs.
Alomari, Omar +2 more
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On maximum degree (signless) Laplacian matrix of a graph
Proyecciones (Antofagasta), 2022 Let G be a simple graph on n vertices and v1, v2, . . . , vn be the vertices ofG. We denote the degree of a vertex vi in G by dG(vi) = di. The maximumdegree matrix of G, denoted by M(G), is the real symmetric matrix withits ijth entry equal to max{di, dj} if the vertices vi and vj are adjacent inG, 0 otherwise.
Rangarajan, R. +2 more
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Bipartite subgraphs and the signless Laplacian matrix
Applicable Analysis and Discrete Mathematics, 2011 For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs.
Steve Kirkland, Debdas Paul
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Some new sharp bounds for the spectral radius of a nonnegative matrix and its application [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we give some new sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. Using these bounds, we obtain some new and improved bounds for the signless Laplacian spectral radius of a graph or a digraph.
Jun He +3 more
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Eigenvalue-based entropy in directed complex networks. [PDF]
PLoS ONE, 2021 Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks.
Yan Sun +3 more
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A Note on the Spectral Radius of Weighted Signless Laplacian Matrix
Advances in Linear Algebra & Matrix Theory, 2018 A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted ...
KAYA GÖK, GÜLİSTAN +2 more
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On the eigenvalues of the distance signless Laplacian matrix of graphs
Proyecciones (Antofagasta)Let G be a connected graph and let DQ(G) be the distance signless Laplacian matrix of G with eigenvalues ρ1≥ ρ2≥…≥ ρn. The spread of the matrix DQ}(G) is defined as s(DQ(G)) := maxi,j| ρi-ρj| = ρ1- ρn. We derive new bounds for the distance signless Laplacian spectral radius ρ1 of G.
Akbar Jahanbani +3 more
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