On spectral radius of the distance matrix

Author: ghec

August undefined, 2024

Web1 de fev. de 2024 · Let G be a simple connected graph, and D(G) be the distance matrix of G. Suppose that $$D_{\max }(G)$$ and $$\lambda _1(G)$$ are the maximum row sum and the spectral radius of D(G), respectively. In this paper, we give a lower bound for … Web10 de abr. de 2024 · The adjacency-distance matrix of G is defined as S(G)=D(G)+A(G). In this paper, S(G) is generalized by the convex lin... The generalized adjacency-distance …

On the distance spectral radius of digraphs with given diameter

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 … 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. … elementary assembly speakers

Note on Generalized Distance Matrix of Graphs

Web3 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) 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 ... 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 … football players helping each other up

Spectral radius of a matrix multiplied by a contraction matrix

On the distance $α$-spectral radius of a connected graph

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 and cite all the research you need on ... Web1 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 … elementary atomic particleWebfor 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 elementary automata knitting pattern

"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 … " - On spectral radius of the distance matrix

On spectral radius of the distance matrix

Mathematics Free Full-Text On the Generalized Distance Energy …

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 ... 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 …

Did you know?

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 $\left\lVert U \right\rVert_{M}$ … 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 …

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 … 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 …

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 … 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 …

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 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 … football player sherman williamsWebPseudo-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 … elementary backstroke historyWeb23 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 … football players high schoolWeb16 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 … elementary avWebDownloadable (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 … elementary atomic structureWeb1 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 … football player shot in dcWeb5 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 … football player shoots self in chest