On the distance spectral radius of trees

Webgeneralized version of the reverse distance matrix and alsostudy its spectral radius for trees with given degree sequence. We prove that the spectral radius is always … Webspectral radius (the largest eigenvalue of the distance matrix) as a molecular descrip-tor giving rise to the extensive QSPR research and to the studies of mathematical properties of the distance spectral radius (DSR). Recently, the extremal trees with respect to the distance spectral radius have been studied by many researchers [10–13].

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WebProof. Let T be a tree in T nwith minimal distance spectral radius. We only need to show that T ˙S;. The case = n 1 is trivial as Tn 1 n= fS g. Suppose that n 2. Then q(T) 2. By Lemma 2.3, q(T) = 2, and then T ˙S n;. Stevanovi´c and Ili ´c [4] conjectured that a complete -ary tree has the minimum distance spectral radius among trees T n. Web7 de jul. de 2015 · Download PDF Abstract: For a tree with the given sequence of vertex degrees the spectral radius of its terminal distance matrix is shown to be bounded from below by the the average row sum of the terminal distance matrix of the, so called, BFS-tree (also known as a greedy tree). This lower bound is typically not tight; nevertheless, … floating boots avis https://chokebjjgear.com

Distance spectral radius of the complements of trees with fixed ...

WebLet D(G) be the distance matrix of a connected graph G.The distance spectral radius of G is the largest eigenvalue of D(G) and it has been proposed to be a molecular structure descriptor.In this article, we determine the unique trees with minimal and maximal distance spectral radii among trees with fixed bipartition. 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 E … WebIndulal in [11] has found sharp bounds on the distance spectral radius and the distance energy of graphs. In [10]Ili´c characterized n-vertex trees with given matching number, which minimize the distance spectral radius. Liu has characterized graphs with minimal distance spectral radius in three floating boombox roblox

Distance spectral radius of the complements of trees

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On the distance spectral radius of trees

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Web15 de abr. de 2013 · Distance spectral radius of graphs with given domination number In this section, we determine the unique tree of given domination number withminimum … Web20 de abr. de 2016 · Ordering trees by their distance spectral radii. Wang and Zhou and Du et al. have considered to order the trees by their distance spectral radii, and …

On the distance spectral radius of trees

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Webgiven domination number, respectively. We determine the unique tree with second maximum -spectral radius among trees, and the unique tree with maximum -spectral radius among trees with given diameter. For a graph with two pendant paths at a vertex or at two adjacent ver-tex, we prove results concerning the behavior of the -spectral radius Web30 de out. de 2024 · We determine the unique graph with minimum distance spectral radius among quasi-trees with xed order and the unique graph with maximum distance …

Web31 de jul. de 2009 · The largest Laplacian spectral radii of trees in $$ \mathcal{T}_{2k + 1} $$ and $$ \mathcal{S}_{2k + 2} $$ and the corresponding trees were given by Guo (2003). ... On distance spectral radius of graphs with given number of pendant paths of fixed length. 19 October 2024. Web5 de dez. de 2024 · Corpus ID: 254246531; Extremal trees with respect to spectral radius of restrictedly weighted adjacency matrices @inproceedings{Zheng2024ExtremalTW, title={Extremal trees with respect to spectral radius of restrictedly weighted adjacency matrices}, author={Ruiling Zheng and Xiaxia Guan and Xian-an Jin}, year={2024} }

Webspectral radius of Coxeter elements. The Coxeter diagram D of (W,S) is the weighted graph whose vertices are the set S, and whose edges of weight m ij join s i to s j when m ij ≥ 3. If D is a tree (such as one of the familiar spherical diagrams A n, B n, D n or E n), then the Coxeter elements w ∈ W range in a single conjugacy class. 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 …

WebThe distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). ... "Distance spectral radius of trees with fixed number of pendent …

WebAbstract. The unique graphs with maximum distance spectral radius among trees with given number of vertices of maximum degree and among homeomorphically irreducible … floating book shelves pegsWeb23 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 the distance matrix and diagonal matrix of the vertex transmissions of , respectively. This paper characterizes the unique graph with minimum generalized distance spectral radius … floating booms to clean oceanWeb1 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, … floating bookshelves bedroomWebconsisting of 1 edges and a path of length n at a common vertex maximizes uniquely the distance spectral radius over all trees of order nwith maximum degree 2. In recent ten years, there are lots of papers on the distance spectral radius, and among them, lots of work was devoted to the distance spectral radius of trees. There is a survey of ... floating boomboxWeb15 de jan. de 2005 · Of all the trees on n vertices and k pendant vertices, the maximal spectral radius is obtained uniquely at T n,k . Proof. We have to proof that if T ∈ T n,k … floating bowel movements meanWeb8 de jul. de 2008 · GUO [Guo, Linear Algebra Appl. 368:379–385, 2003.] determined the largest value of Laplacian spectral radii μ(T) of the trees T in $${\mathcal{T}(2k)}$$ and gave the corresponding tree T in $${\mathcal{T}(2k)}$$ whose ;μ(T) reaches ... On distance spectral radius of graphs with given number of pendant paths of fixed length. 19 ... floating boombox coolerWeb1 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 … great hollywood movies ted sennett