On spectral radius of the distance matrix
WebLet ∂ 1 ( G) ≥ ∂ 2 ( G) ≥ ⋯ ≥ ∂ n ( G) be the eigenvalues of D α ( G) and let S D α ( G) = ∂ 1 ( G) − ∂ n ( G) be the generalized distance spectral spread of the graph G. In this … 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 …
On spectral radius of the distance matrix
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WebThe distance spectral radius . λ (G) of a strongly connected digraph G is the eigenvalue of its distance matrix . D (G) with the largest modulus. Let G n d denote the set of strongly … 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 set. de 2013 · Let G be a connected graph and D(G) = (d ij ) be the distance matrix of G where d ij is the length of a shortest path between v i and v j .ThematrixD(G) is nonnegative and irreducible, so the eigenvalues of D(G) ... Sharp bounds on the distance spectral radius and the distance energy of graphs. Linear Algebra Appl., 430 (2009), pp ... Web25 de dez. de 2024 · There is a survey of Aouchiche and Hansen [1] in 2014 on the relevant background and results on the spectrum of the distance matrix of a graph, and especially on the distance spectral radius.
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 ... 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 …
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 …
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 … how to send my official transcriptsWebPrincess Elisabeth Antarctica (PEA) is a polar research base owned by the Belgian government and managed by the International Polar Foundation (IPF), located at a latitude of 71 ∘ 56 ′ 59.64 ′′ S and a longitude of 23 ∘ 20 ′ 49.56 ′′ E. The station was built on the Utsteinen Nunatak in the immediate vicinity of the Sør Rondane Mountains, a mountain … how to send music from laptop to iphoneWebfor 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 how to send my amc nft to metamask walletWeb1 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 send my joycons to nintendoWeb19 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 … how to send multiple texts androidWebFind the distance between each pair of observations in X by using the pdist and squareform functions with the default Euclidean distance metric. dist_temp = pdist (X); dist = squareform (dist_temp); Construct the similarity matrix and confirm that it is symmetric. S = exp (-dist.^2); issymmetric (S) ans = logical 1. Perform spectral clustering. how to send my gmat scores to schoolsWeb1 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 send my transcript to college