On spectral radius of the distance matrix
WebThe spectral radius is closely related to the behavior of the convergence of the power sequence of a matrix; namely as shown by the following theorem. Theorem. Let A ∈ Cn×n with spectral radius ρ(A). Then ρ(A) < 1 if and only if. On the other hand, if ρ(A) > 1, . The statement holds for any choice of matrix norm on Cn×n . 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 …
On spectral radius of the distance matrix
Did you know?
Web5 de mar. de 2014 · Spectral properties of line distance matrices, associated with biological sequences, are studied. It is shown that a line distance matrix of size n>1 has one … Web24 de mar. de 2024 · Let A be an n×n matrix with complex or real elements with eigenvalues lambda_1, ..., lambda_n. Then the spectral radius rho(A) of A is …
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 ... WebFind 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.
Web15 de jul. de 2014 · The spectral radius of A, denoted by λ ( A), is the largest modulus of eigenvalues of A. Furthermore, if A is irreducible, then λ ( A) is just the largest eigenvalue of A. Let G be a simple graph with vertex set V ( G) = { v 1, v 2, …, v n }. Let A ( G) = ( a ij) n × n be the ( 0 1) –adjacency matrix of G, where a ij = 1 if v i and v j ... 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 …
http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/viewFile/5783/354355157
Web9 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 … how many times should i do laundryWebmultipartite 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 many times should i forgive bibleWebThe 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 … how many times should i deadlift a weekWeb21 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 … how many times should i forgive my brotherWeb1 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 … how many times should i feed my cat wet foodWeb1 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 … how many times should i forgive scriptureWeb14 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 ... how many times should i go to the gym a week