Results 1 to 10 of about 13,572 (222)
Trees with matrix weights: Laplacian matrix and characteristic-like vertices [PDF]
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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The bipartite Laplacian matrix of a nonsingular tree
Special Matrices, 2023 For a bipartite graph, the complete adjacency matrix is not necessary to display its adjacency information. In 1985, Godsil used a smaller size matrix to represent this, known as the bipartite adjacency matrix.
Bapat Ravindra B. +2 more
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The signless Laplacian matrix of hypergraphs
Special Matrices, 2022 In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph ...
Cardoso Kauê, Trevisan Vilmar
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The third smallest eigenvalue of the Laplacian matrix [PDF]
The Electronic Journal of Linear Algebra, 2001 It is well known that the second smallest eigenvalue of the Laplacian of a graph bears a lot of information about combinatorial properties of the graph. In this paper, the relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored.
Sukanta Pati
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Correction to: Robust joint clustering of multi-omics single-cell data via multi-modal high-order neighborhood Laplacian matrix optimization. [PDF]
Bioinformatics, 2023 europepmc +3 more sources
Permanent of the laplacian matrix of trees with a given matching
Discrete Mathematics, 1986 Let \(G=(V,E)\) be an arbitrary graph, and \(d_ i>0\) be the degree of the vertex \(v_ i\in V\). D(G) denotes the diagonal matrix whose (i,i)-entry is \(d_ i\), and A(G) denotes the adjacency matrix of the graph G. The matrix \(L(G)=D(G)-A(G)\) will be called the Laplacian matrix of the graph G.
John Goldwasser
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Interlacing Properties of Eigenvalues of Laplacian and Net-Laplacian Matrix of Signed Graphs
, 2023 This paper explores interlacing inequalities in the Laplacian spectrum of signed cycles and investigates interlacing relationship between the spectrum of the net-Laplacian of a signed graph and its subgraph formed by removing a vertex together with its incident edges.
Satyam Guragain, Ravi Srivastava
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The spectrum of the Laplacian matrix of a balanced binary tree
Linear Algebra and its Applications, 2002 Let \(L({\mathcal B}_k)\) be the Laplacian matrix of an unweighted balanced binary tree \({\mathcal B}_k\) of \(k\) levels. The author completely characterizes the eigenvalues of \(L({\mathcal B}_k)\) by labelling vertices of \({\mathcal B}_k\) in such a way that \(L({\mathcal B}_k)\) becomes a symmetric persymmetric matrix.
Óscar Rojo
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Generalized inverse of the Laplacian matrix and some applications [PDF]
Bulletin: Classe des sciences mathematiques et natturalles, 2004 The generalized inverse L? of the Laplacian matrix of a connected graph is examined and some of its properties are established. In some physical and chemical considerations the quantity rij = {L?)ii + (L?)jj ? (L?)ij - (L?)ji is encountered; it is called resistance distance. Based on the results obtained for L? we prove some previously known and deduce
İvan Gutman, Wen Xiao
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The spectra of the adjacency matrix and Laplacian matrix for some balanced trees
Linear Algebra and its Applications, 2005 The authors express the spectra of the adjacency and the Laplacian matrices of an unweighted rooted tree of \(k\) levels, such that in each level the vertices have the same degree, in terms of the spectra of a set of symmetric tridiagonal matrices.
Óscar Rojo, Ricardo L. Soto
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