On the distance spectral radius of trees
Web23 de out. de 2013 · For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix. In this paper, of all trees with both given order and … 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].
On the distance spectral radius of trees
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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. Web1 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 …
Web1 de mar. de 2010 · We determine the unique tree that maximizes (respectively minimizes) the distance spectral radius over all trees on n vertices with k pendant paths of length … WebFor trees and unicyclic graphs, distance energy is equal to the doubled value of the distance spectral radius. In this paper, we introduce a general transformation that …
Web28 de ago. de 2010 · The distance spectral radius of , denoted as , is the largest eigenvalue of the distance matrix . Distance energy is a newly introduced molecular … 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
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} }
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. north andesWeb15 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 … how to replace a faucet cartridgeWebeigenvalue is also equal to the spectral radius of D(G), which is also called the distance spectral radius of G. When G is a tree, the spectral radius is in fact the only positive … how to replace a fiberglass tubWeb14 de ago. de 2024 · Nath, M., Paul, S.: On the distance spectral radius of bipartite graphs. Linear Algebra Appl. 436, 1285–1296 (2012) Article MathSciNet Google Scholar Nath, M., Paul, S.: On the distance spectral radius of trees. Linear Multilinear Algebra 61, 847–855 (2013) Article MathSciNet Google Scholar how to replace a fireboxWeb2 de jan. de 2024 · A note on distance spectral radius of trees. Authors. Yanna Wang; Rundan Xing; Bo Zhou; Fengming Dong; Publication date 2024. Publisher Walter de Gruyter GmbH. Doi DOI: 10.1515/spma-2024-0021. Abstract Abstract is not available. journal-article; Similar works. Full text. Crossref Provided original full text link. how to replace a faulty light switchWebspectral 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. north anderson church of godWeb6 de ago. de 2012 · In this article, we prove that among trees on n vertices and matching number m, the dumbbell . is the unique tree that maximizes the distance spectral radius, which was conjectured by Aleksandar Ilić [Distance spectral radius of trees with given … how to replace a fireplace