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The (distance) signless Laplacian spectral radius of digraphs with given arc connectivity

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2019, Volume 581, pp. 85 - 111

Let G‾n,k denote the set of strongly connected digraphs with order n and arc connectivity k, and let G‾n,k⁎ denote the set of digraphs in G‾n,k with all...

Signless Laplacian spectral radius | Arc connectivity | Strongly connected | Distance signless Laplacian spectral radius | MATHEMATICS | MATRIX | MATHEMATICS, APPLIED | SHARP UPPER | BOUNDS | GRAPHS | Input output | Spectra | Graph theory | Apexes

Signless Laplacian spectral radius | Arc connectivity | Strongly connected | Distance signless Laplacian spectral radius | MATHEMATICS | MATRIX | MATHEMATICS, APPLIED | SHARP UPPER | BOUNDS | GRAPHS | Input output | Spectra | Graph theory | Apexes

Journal Article

Discrete Mathematics, ISSN 0012-365X, 03/2019, Volume 342, Issue 3, pp. 643 - 653

Given a connected graph G, the Randić index R(G) is the sum of (d(u)d(v))−1∕2 over all edges {u,v} of G, where d(u) and d(v) are the degrees of vertices u and...

Randić index | Eigenvalue | Signless Laplacian matrix | MATHEMATICS | Randic index | DIAMETER | BOUNDS | CONJECTURES | MOLECULAR CONNECTIVITY | EXTREMAL GRAPHS

Randić index | Eigenvalue | Signless Laplacian matrix | MATHEMATICS | Randic index | DIAMETER | BOUNDS | CONJECTURES | MOLECULAR CONNECTIVITY | EXTREMAL GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2017, Volume 227, pp. 136 - 141

Let q(G) and μ(G) denote the signless Laplacian and distance signless Laplacian spectral radius of a digraph G, respectively. In this paper, we characterize...

Signless Laplacian | Distance signless Laplacian | Dichromatic number | Spectral radius | Vertex connectivity | GRAPH | MATHEMATICS, APPLIED | STRONGLY CONNECTED DIGRAPHS

Signless Laplacian | Distance signless Laplacian | Dichromatic number | Spectral radius | Vertex connectivity | GRAPH | MATHEMATICS, APPLIED | STRONGLY CONNECTED DIGRAPHS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2010, Volume 432, Issue 2, pp. 566 - 570

We give tight conditions on the signless Laplacian spectral radius of a graph for the existence of Hamiltonian paths and cycles.

Hamiltonian cycle | Signless Laplacian spectral radius | Hamiltonian path | GRAPH | MATHEMATICS, APPLIED | SUM | SQUARES

Hamiltonian cycle | Signless Laplacian spectral radius | Hamiltonian path | GRAPH | MATHEMATICS, APPLIED | SUM | SQUARES

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2018, Volume 553, pp. 117 - 128

Let G be a k-connected irregular graph with n vertices, m edges, maximum degree Δ and minimum degree δ. In this paper, we mainly...

Signless Laplacian spectral radius | Maximum degree | Irregular graph | Spectral radius | k-Connected graph | MATHEMATICS | MATHEMATICS, APPLIED | LARGEST EIGENVALUE | BOUNDS | NONREGULAR GRAPHS

Signless Laplacian spectral radius | Maximum degree | Irregular graph | Spectral radius | k-Connected graph | MATHEMATICS | MATHEMATICS, APPLIED | LARGEST EIGENVALUE | BOUNDS | NONREGULAR GRAPHS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2017, Volume 529, pp. 271 - 293

We determine the unique hypergraphs with minimum distance Laplacian spectral radius among connected k-uniform hypergraphs and k-uniform hypertrees,...

Uniform hypertree | Distance Laplacian spectral radius | Uniform hypergraph | Graft transformation | Distance matrix | Distance signless Laplacian spectral radius | MATHEMATICS | EIGENVALUES | MATRIX | MATHEMATICS, APPLIED | SHARP BOUNDS | GRAPHS

Uniform hypertree | Distance Laplacian spectral radius | Uniform hypergraph | Graft transformation | Distance matrix | Distance signless Laplacian spectral radius | MATHEMATICS | EIGENVALUES | MATRIX | MATHEMATICS, APPLIED | SHARP BOUNDS | GRAPHS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2010, Volume 432, Issue 9, pp. 2257 - 2272

A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This...

Graph spectra | Signless Laplacian | Adjacency matrix | Graph theory | Laplacian | MATHEMATICS, APPLIED | MATCHING NUMBER | RADIUS | TREES

Graph spectra | Signless Laplacian | Adjacency matrix | Graph theory | Laplacian | MATHEMATICS, APPLIED | MATCHING NUMBER | RADIUS | TREES

Journal Article

Discrete Optimization, ISSN 1572-5286, 05/2019, Volume 32, pp. 63 - 72

Let G=(V(G),E(G)) be a weighted digraph with vertex set V(G)={v1,v2,…,vn} and arc set E(G), where the arc weights are nonzero nonnegative symmetric matrices....

Signless Laplacian spectral radius | Upper bound | Weighted digraph

Signless Laplacian spectral radius | Upper bound | Weighted digraph

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 04/2019, Volume 566, pp. 98 - 120

Let G be an undirected simple graph. The signless Laplacian spread of G is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This...

Signless Laplacian spread | Matrix spread | Signless Laplacian matrix | MATHEMATICS | MATHEMATICS, APPLIED | BIPARTITENESS | ALGEBRAIC CONNECTIVITY | SPECTRAL-RADIUS | GRAPHS | Eigenvalues | Lower bounds | Invariants

Signless Laplacian spread | Matrix spread | Signless Laplacian matrix | MATHEMATICS | MATHEMATICS, APPLIED | BIPARTITENESS | ALGEBRAIC CONNECTIVITY | SPECTRAL-RADIUS | GRAPHS | Eigenvalues | Lower bounds | Invariants

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2017, Volume 293, pp. 218 - 225

Let ρ(D(G)) denote the distance spectral radius of a graph G and ∂(G→) denote the distance signless Laplacian spectral radius of a digraph G→. Let Gn,kD be the...

Distance signless Laplacian matrix | Dichromatic number | Spectral radius | Distance matrix | EIGENVALUES | MATRIX | MATHEMATICS, APPLIED | NUMBER | CONNECTIVITY

Distance signless Laplacian matrix | Dichromatic number | Spectral radius | Distance matrix | EIGENVALUES | MATRIX | MATHEMATICS, APPLIED | NUMBER | CONNECTIVITY

Journal Article

Discrete Mathematics, Algorithms and Applications, ISSN 1793-8309, 06/2018, Volume 10, Issue 3

Journal Article

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Full Text
Sharp bounds for ordinary and signless Laplacian spectral radii of uniform hypergraphs

Applied Mathematics and Computation, ISSN 0096-3003, 07/2016, Volume 285, pp. 217 - 227

We give sharp upper bounds for the ordinary spectral radius and signless Laplacian spectral radius of a uniform hypergraph in terms of the average 2-degrees or...

Eigenvalues of tensors | Average 2-degree | Signless Laplacian tensor | Tensor | Uniform hypergraph | Adjacency tensor | EIGENVALUES | TENSORS | MATHEMATICS, APPLIED | Lower bounds | Mathematical models | Spectra | Upper bounds | Computation

Eigenvalues of tensors | Average 2-degree | Signless Laplacian tensor | Tensor | Uniform hypergraph | Adjacency tensor | EIGENVALUES | TENSORS | MATHEMATICS, APPLIED | Lower bounds | Mathematical models | Spectra | Upper bounds | Computation

Journal Article

Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 3/2018, Volume 49, Issue 1, pp. 113 - 127

Let $$\vec G$$ G → be a strongly connected digraph and Q( $$\vec G$$ G → ) be the signless Laplacian matrix of $$\vec G$$ G → . The spectral radius of Q(...

{\tilde \infty _1}$$ ∞ ˜ 1 -digraph | {\tilde \theta _2}$$ θ ˜ 2 -digraph | {\tilde \infty _2}$$ ∞ ˜ 2 -digraph | Numerical Analysis | Mathematics, general | Mathematics | Applications of Mathematics | The signless Laplacian spectral radius | {\tilde \theta _1}$$ θ ˜ 1 -digraph | θ | digraph | ∞ | MATHEMATICS | TREES | he signless Laplacian spectral radius | (infinity)over-tilde-digraph | (theta)over-tilde-digraph | GRAPHS | Analysis | Graph theory

{\tilde \infty _1}$$ ∞ ˜ 1 -digraph | {\tilde \theta _2}$$ θ ˜ 2 -digraph | {\tilde \infty _2}$$ ∞ ˜ 2 -digraph | Numerical Analysis | Mathematics, general | Mathematics | Applications of Mathematics | The signless Laplacian spectral radius | {\tilde \theta _1}$$ θ ˜ 1 -digraph | θ | digraph | ∞ | MATHEMATICS | TREES | he signless Laplacian spectral radius | (infinity)over-tilde-digraph | (theta)over-tilde-digraph | GRAPHS | Analysis | Graph theory

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 07/2017, Volume 305, pp. 166 - 173

The unique graphs with maximum spectral radius and signless Laplacian spectral radius are determined among trees, unicyclic graphs and bicyclic graphs...

Branch vertex | Signless Laplacian spectral radius | Tree | Unicyclic graph | Bicyclic graph | Spectral radius | MATHEMATICS, APPLIED | BOUNDED NUMBER | SPANNING-TREES | INDEX

Branch vertex | Signless Laplacian spectral radius | Tree | Unicyclic graph | Bicyclic graph | Spectral radius | MATHEMATICS, APPLIED | BOUNDED NUMBER | SPANNING-TREES | INDEX

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 07/2014, Volume 238, pp. 43 - 49

Let G=(V,E) be a digraph with n vertices and m arcs without loops and multiarcs, and vertex set V={v1,v2,…,vn}. Denote the outdegree and average 2-outdegree of...

Digraph | Signless Laplacian | Spectral radius | MATHEMATICS, APPLIED | Mathematical models | Graph theory | Spectra | Computation

Digraph | Signless Laplacian | Spectral radius | MATHEMATICS, APPLIED | Mathematical models | Graph theory | Spectra | Computation

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2014, Volume 457, pp. 93 - 113

Let D be a strongly connected digraph and A(D) be the adjacency matrix of D. Let diag(D) be the diagonal matrix with outdegrees of the vertices of D and...

Signless Laplacian | Clique number | Digraph | Girth | Spectral radius | Vertex connectivity | MATHEMATICS, APPLIED | NUMBER | BOUNDS

Signless Laplacian | Clique number | Digraph | Girth | Spectral radius | Vertex connectivity | MATHEMATICS, APPLIED | NUMBER | BOUNDS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 04/2017, Volume 519, pp. 327 - 342

A bag Bagp,q is a graph obtained from a complete graph Kp by replacing an edge uv by a path Pq. In this paper, we show that for all the connected graphs of...

Signless Laplacian index | Radius | Graph | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | BOUNDS | CONJECTURES | SPECTRAL-RADIUS

Signless Laplacian index | Radius | Graph | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | BOUNDS | CONJECTURES | SPECTRAL-RADIUS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2013, Volume 439, Issue 12, pp. 3955 - 3963

The unique graphs with minimum and second-minimum distance (distance signless Laplacian, respectively) spectral radii are determined among bicyclic graphs with...

Distance signless Laplacian matrix | Bicyclic graph | Transmission | Distance spectral radius | Distance signless Laplacian spectral radius | Distance matrix | MATRIX | MATHEMATICS, APPLIED | NUMBER | TREES | VERTEX

Distance signless Laplacian matrix | Bicyclic graph | Transmission | Distance spectral radius | Distance signless Laplacian spectral radius | Distance matrix | MATRIX | MATHEMATICS, APPLIED | NUMBER | TREES | VERTEX

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 11/2019, Volume 67, Issue 11, pp. 2307 - 2324

Let , and be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where denotes the...

independence number | domination number | Distance Laplacian eigenvalues | diameter | distance signless Laplacian eigenvalues | MATHEMATICS | MATRIX | SPECTRAL-RADIUS | Eigenvalues | Eigen values

independence number | domination number | Distance Laplacian eigenvalues | diameter | distance signless Laplacian eigenvalues | MATHEMATICS | MATRIX | SPECTRAL-RADIUS | Eigenvalues | Eigen values

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 8/2019, Volume 14, Issue 4, pp. 693 - 713

Suppose that the vertex set of a graph G is V(G) = {v 1, v 2,…, v n }. The transmission Tr(v i ) (or D i ) of vertex v i is defined to be the sum of distances...

Graph | 05C50 | Mathematics, general | distance signless Laplacian spectral radius | Mathematics | second largest eigenvalue of distance signless Laplacian matrix | spread | MATHEMATICS | BOUNDS | SPECTRAL-RADIUS | Eigenvalues | Lower bounds | Graphs | Trees (mathematics) | Spectra | Apexes

Graph | 05C50 | Mathematics, general | distance signless Laplacian spectral radius | Mathematics | second largest eigenvalue of distance signless Laplacian matrix | spread | MATHEMATICS | BOUNDS | SPECTRAL-RADIUS | Eigenvalues | Lower bounds | Graphs | Trees (mathematics) | Spectra | Apexes

Journal Article

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