On spectral radius of the distance matrix

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August undefined, 2024

Web23 de jan. de 2024 · The generalized distance spectral radius of a connected graph is the spectral radius of the generalized distance matrix of , defined by where and denote … Web23 de jan. de 2010 · Abstract. For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the sum …

A Proof of a Conjecture on the Distance Spectral Radius and …

Web2 de mar. de 2024 · The nodes are uniformly distributed in a ring coverage area specified by the inner radius R 1 and outer radius R 2, where CT is located at the origin. Taking into account the wireless fading channel model—that is, when the transmit power at the transmitter is P t —the received power at the receiver is P r = P t d − α , where d is the … Web16 de dez. de 2024 · The eccentricity matrix . ϵ (G) of a connected graph G is obtained from the distance matrix of G by retaining the largest distance in each row and each column and setting the remaining entries as 0. The eccentricity matrices of graphs are closely related to the distance matrices of graphs, nevertheless a number of properties of … how to store logs for wood burner

Spectral radius of a matrix multiplied by a contraction matrix

WebDownloadable (with restrictions)! Let G be a connected graph. The greatest eigenvalue and the spread of the sum of the adjacency matrix and the distance matrix of G are called the adjacency-distance spectral radius and the adjacency-distance spread of G, respectively. Both quantities are used as molecular descriptors in chemoinformatics. We … Web1 de jul. de 2010 · The greatest eigenvalue of a line distance matrix D, denoted by λ(D), is called the spectral radius of D. In this paper, we obtain some sharp upper and lower … Web1 de mar. de 2024 · Let C be a symmetric matrix. On spectral radius of the extended adjacency matrix. In this section we give some lower and upper bounds on η 1. … how to store logs outdoors

The generalized adjacency-distance matrix of connected graphs

The distance spectral radius of trees Request PDF - ResearchGate

Web1 de out. de 2010 · Anatomy Radius On spectral radius of the distance matrix CC BY 4.0 Authors: Liu Zhongzhu Huizhou University Abstract We characterize graphs with minimal … Web1 de mar. de 2024 · The adjacency matrix A = A ( G) of the graph G is defined so that its ( i, j )-entry is equal to 1 if vivj ∈ E ( G) and 0 otherwise. Let λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n − 1 ≥ λ n denote the eigenvalues of A ( G ). The greatest eigenvalue λ1 is usually referred to as the spectral radius of the graph G. The energy of the graph G is defined ... how to store long integer in cWebmultipartite graphs. Later in the paper are given some sharp bounds for generalized distance spectral radius of connected graphs. MSC: 05C50; 05C12; 15A18 Keywords: distance -spectral radius; bounds on D -spectral radius; transmission matrix Submission date: 21.11.2024 / Acceptance date: 11.11.2024 1.Introduction how to store long handled tools

"Webfor all positive integers r, where ρ(A) is the spectral radius of A. For symmetric or hermitian A, we have equality in for the 2-norm, since in this case the 2-norm is precisely the … " - On spectral radius of the distance matrix

On spectral radius of the distance matrix

On the distance Laplacian spectral radius of bicyclic graphs

WebThe generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy … Web15 de abr. de 2013 · The distance matrix of G is defined as D (G) = (d uv ) u,vâˆˆV (G) .The eigenvalues of D (G) are called the distance eigenvalues of G.SinceD (G) is real and …

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Web5 de dez. de 2024 · The weighted adjacency matrix A f ( G ) of a graph G is a square matrix, where the ( i , j ) -entry is equal to f ( d i , d j ) if the vertices v i and v j are adjacent and 0 otherwise. Li and Wang [22] tried to unify methods to study spectral radius of weighted adjacency matrices of graphs weighted by various topological indices. Web25 de jun. de 2024 · where x is a vector of size m. I have experiments for randomly initialized matrices that satisfy the above conditions. All of these matrices have spectral radii less than or equal to 1. For the case when the spectral radius is equal to 1, the process still converges in my experiment. (Note that the matrix ( A T E) k converges to a non-zero ...

Web1 de ago. de 2010 · The distance spectral radius @r (G) of a graph G is the largest eigenvalue of the distance matrix D (G). Recently, many researches proposed the use of @r (G) as a molecular structure descriptor of alkanes. In this paper, we introduce general transformations that decrease distance spectral radius and characterize n-vertex trees …

Web23 de jan. de 2024 · Corpus ID: 119323032; On the generalized distance spectral radius of graphs @article{Cui2024OnTG, title={On the generalized distance spectral radius of … Web19 de jun. de 2024 · In this article, we introduce a Laplacian for the reciprocal distance matrix of a connected graph, called the reciprocal distance Laplacian. Let $$\\delta …

Web1 de dez. de 2011 · The distance spectral radius Ï (G) = Ï G of G is the largest eigenvalue of the distance matrix D of the graph G. Distance energy DE (G) is a newly …

Web22 de fev. de 2024 · Extremal values for the spectral radius of the normalized distance Laplacian. Jacob Johnston, Michael Tait. The normalized distance Laplacian of a graph is defined as where is the matrix with pairwise distances between vertices and is the diagonal transmission matrix. In this project, we study the minimum and maximum spectral radii … read-depth ratioWeb3 de abr. de 2024 · In this paper, we present two suffcient conditions in terms of the distance signless Laplacian sepectral radius for the exsitence of perfect matchings in graphs and bipatite graphs. Subjects: Combinatorics (math.CO) how to store long character in cWeb10 de abr. de 2024 · The adjacency-distance matrix of G is defined as S(G)=D(G)+A(G).... Find, read and cite all the research you need on ResearchGate. Article. The … how to store long beansWebThe distance Laplacian matrix of a connected graph G is defined as L(G)=Tr(G)−D(G), where Tr(G) is the diagonal matrix of the vertex transmissions in G and D(G) is the … read-only 1WebPseudo-Anosovs of interval type Ethan FARBER, Boston College (2024-04-17) A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional … read-line racketWeb14 de jun. de 2024 · In this paper we give some graft transformations on distance signless Laplacian spectral radius of the graphs and use them to characterize the graphs with the minimum and maximal distance signless ... Spectral properties of distance matrix of graphs, in: I. Gutman, B. Furtula (Eds), Distance in Molecular graphs Theory, in ... read-onlyWeb1 de jan. de 2008 · In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also ... how to store layer cake for future use