On spectral radius of the distance matrix

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August undefined, 2024

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 ... WebPrincess 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 …

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

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 … Webmultipartite 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 are tubes inserted into ears

Distance spectral radius of graphs with r pendent vertices

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 … 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 … 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 ... how are tsunami waves formed

The generalized adjacency-distance matrix of connected graphs

Spectral radius - Wikipedia

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 $\left\lVert U \right\rVert_{M}$ … Web1 de fev. de 2024 · In [], Atik and Panigrahi presented some bounds for spectral radius of distance matrix of a graph.They also introduced a class of graphs called DVDR graphs for characterizing equality in these bounds. A connected graph G on n vertices is said to be distinguished vertex deleted regular graph (DVDR) if there exist a vertex v in G such that … how are tsunamis created how many minutes are in 9 1/4 hours

"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 … " - On spectral radius of the distance matrix

On spectral radius of the distance matrix

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

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 … 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 …

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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 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. …

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 … 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 .

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 … http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/viewFile/5783/354355157

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 ...

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 … how are tsunamis related to earthquakesWeb10 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 generalized adjacency-distance matrix of connected ... how many minutes are in 9.5 hoursWebThe 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 … how are tufa towers formedWeb22 de set. de 2013 · We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices associated with a graph, including the adjacency matrix, the signless Laplacian matrix, … how many minutes are in 900 secondsWebfor 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 … how many minutes are in a basketball gameWebdistance 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 … how are tubs attachedWeb1 de mar. de 2012 · The spectral distance Ïƒ (G 1 , G 2 ) between n vertex graphs G 1 and G 2 is defined by Ïƒ (G 1 , G 2 ) = n âˆ‘ i=1 Î» i (G 1 )âˆ’ Î» i (G 2 ) . Here we provide … how many minutes are in a basketball quarter