On spectral radius of the distance matrix

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 … 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 …

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Web1 de mar. de 2012 · DOI: 10.1016/j.aml.2011.09.007 Corpus ID: 34853737; Some graft transformations and its applications on the distance spectral radius of a graph @article{Yu2012SomeGT, title={Some graft transformations and its applications on the distance spectral radius of a graph}, author={Guanglong Yu and Huicai Jia and … WebThe 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 distance matrix of G. The la... share laptop screen to chromecast https://bowlerarcsteelworx.com

The Spectral Radius of the Reciprocal Distance Laplacian Matrix of …

WebIn mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. [1] More generally, the spectral radius of a bounded linear … Web21 de nov. de 2024 · Accepted: 27 May 2024. Abstract. The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. In this paper, we give several less restricted graft transformations that decrease the distance spectral radius, and determine the unique graph with minimum distance spectral radius among home … Web17 de jan. de 2024 · How to prove that the spectral radius of a linear operator is the infimum over all subordinate norms of the corresponding norm of the operator. So along those lines $$ \rho(AU) = \inf_{\left\lVert \cdot \right\rVert} \left\lVert AU \right\rVert $$ Just suppose for a second that the infimum is achieved and let $\left\lVert U \right\rVert_{M}$ … poor kids frontline

Distance spectral radius of the complements of trees

Category:Spectral radius of a matrix multiplied by a contraction matrix

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On spectral radius of the distance matrix

On spectral radius and energy of extended adjacency matrix of …

Web1 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 ... 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 ...

On spectral radius of the distance matrix

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Web1 de abr. de 2024 · Download Citation On Apr 1, 2024, Kang Liu and others published Distance spectral radius of the complements of trees with fixed parameters Find, read … Web1 de jan. de 2013 · We determine the graphs with maximal spectral radius of the complementary distance matrix among simple connected graphs with fixed order and …

WebThe 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 … 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 …

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 spectral radius of A. For an arbitrary matrix, we may not have equality for any norm; a counterexample would be Web1 de mar. de 2012 · The spectral distance σ (G 1 , G 2 ) between n vertex graphs G 1 and G 2 is defined by σ (G 1 , G 2 ) = n ∑ i=1 λ i (G 1 )− λ i (G 2 ) . Here we provide …

Web1 de abr. de 2012 · The distance spectral radius of a connected graph G, denoted by ρ (G), is the maximal eigenvalue of the distance matrix of G. In this paper we find a sharp lower bound as well as a sharp upper ...

Web29 de jan. de 2024 · For a connected graph and , the distance -spectral radius of is the spectral radius of the matrix defined as , where is a diagonal matrix of vertex transmissions of and is the distance matrix of . We give bounds for the distance -spectral radius, especially for graphs that are not transmission regular, propose some graft … poor kids in the philippinesWeb23 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 … poor kids school ok m californiaWeb9 de dez. de 2024 · Abstract. The distance Laplacian matrix of a connected graph is defined as , where is the distance matrix of and is the diagonal matrix of vertex transmissions of . The largest eigenvalue of is called the distance Laplacian spectral radius of . In this paper, we determine the graphs with maximum and minimum distance … poor kids in trailer parkWeb5 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. poor kids should clean up school for lunchWeb23 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 … poor kids\u0027 educationWeb2 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 … share laptop screen via hdmiWebdistance spectral radius of graphs and bipartite graphs, lower bounds for the distance energy of graphs, and characterize the extremal graphs. We also discuss upper bounds … share laptop screen to another laptop