Ordering trees by their abc spectral radii

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August undefined, 2024

WebThe ABC spectral radius of G is the largest eigenvalue of M(G). In the present paper, two graph perturbations with respect to ABC spectral radius are established. By applying these perturbations, the trees with the third, fourth, and fifth largest ABC spectral radii are determined. ... Ordering trees by their ABC spectral radii. Wenshui Lin ... WebThe trees with maximum and minimum ABC spectral radius are characterized. Also, in the class of trees on n vertices, we obtain the trees having first four values of ABC spectral radius and subsequently derive a better upper bound. Keywords tree, ABC matrix, ABC spectral radius, nonnegative matrix Full Text: PDF

Free Full-Text On the Aα-Spectral Radii of Cactus Graphs - MDPI

WebMay 28, 2024 · The -spectral radius of a cactus graph with n vertices and k cycles is explored. The outcomes obtained in this paper can imply some previous bounds from trees to cacti. In addition, the corresponding extremal graphs are determined. Furthermore, we proposed all eigenvalues of such extremal cacti. WebOct 31, 2024 · Two graph perturbations with respect to ABC spectral radius are established. Consequently, the trees of order at least 10 with the 1st to 5th largest ABC spectral radii are... did mars have air

Arithmetic-geometric matrix of graphs and its applications

WebOct 31, 2024 · The ABC spectral radius of G is the largest eigenvalue of M(G). In the present paper, two graph perturbations with respect to ABC spectral radius are established. By applying these perturbations, the trees with the third, fourth, and fifth largest ABC spectral … WebApr 20, 2016 · Ordering trees by their distance spectral radii Wang and Zhou [19] and Du et al. [5] have considered to order the trees by their distance spectral radii, and determined the first three trees with small distance spectral radius. Lemma 3.1 [5], [19] Let T ∉ { S n, S n − 2, 2, S n − 3, 3 } be a tree on n ≥ 6 vertices. WebWe study the spectrum of Laplacian for trees, and make an approach to ordering trees by the spectral radius of Laplacian. A general method of ordering trees is derived as well, and as its applications, we give the optimal estimates of the orderings of two types of trees. did mars have a civilization

Ordering trees by their largest eigenvalues - ScienceDirect

Ordering Trees by Their ABC Spectral Radii Request PDF

WebWe study the spectrum of Laplacian for trees, and make an approach to ordering trees by the spectral radius of Laplacian. A general method of ordering trees is derived as well, and as its applications, we give the optimal estimates of the orderings of two types of trees. Sign InHelp Email PasswordForgot your password? Show WebFrom our farm to your front door. Shop our huge inventory of trees, shrubs & plants for sale. Free shipping on qualified orders. Call us today 1-888-329-0140 did marshall win yesterdayWebJan 11, 2024 · order, size and spectral radius of G. Zheng et al. [6, 7] derived AG spectral radius of trees and unicyclic graphs and determined extremal values on AG spectral radius of trees independently. Later, Zheng and Jin [8] characterized unicyclic graphs of order n ≥ 5 with the smallest and ﬁrst four largest AG spectral radii detailly. The upper did marsha p johnson throw the first brick

"WebOct 15, 2006 · Fig. 3. Trees T 1 , T 2 , T 3 and T 4 . 456 W. Lin, X. Guo / Linear Algebra and its Applications 418 (2006) 450–456 Theorem 4.1. When n greaterorequalslant 12, in the order of trees in T n by their largest eigenvalues, trees S 9 n , S 10 n ,S 11 n ,S 12 n and S 13 n take the 9th to 13th positions, respectively. " - Ordering trees by their abc spectral radii

Ordering trees by their abc spectral radii

Arithmetic-geometric matrix of graphs and its applications

Webtrees with ﬁrst four largest values of the ABCspectral radius, in the class of trees on nvertices. Subsequently, we are able to provide a better upper bound on the ABCspectral radius of trees. 2. Main results Let Aand Bbe two square matrices of same size. We say, Adominates B, write it as A B or B Aif A Bis a nonnegative matrix. Webwith the largest ABC spectral radius among all cactus graphs with ﬁxed order and number of ... [14] W. LIN,Z.YAN,P.FU AND J. LIU, Ordering trees by their ABC spectral radii, Int. J. Quantum. Chem. 121, (2024), e26519. [15] Y. YUAN ANDZ. DU, The ﬁrst two maximum ABC spectral radii of bicyclic graphs, Linear Algebra

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WebThe ABC spectral radius of G is the largest eigenvalue of M(G). In the present paper, two graph perturbations with respect to ABC spectral radius are established. By applying these perturbations, the trees with the third, fourth, and fifth … WebMar 1, 2024 · The ABC matrix of a graph G, recently introduced by Estrada, is the square matrix of order whose -entry is equal to if the -th vertex and the -th vertex of G are adjacent, and 0 otherwise, where is the degree of the -th vertex of G ABC spectral radius G is the largest eigenvalue of the ABC matrix of , which is denoted by .

WebThe ABC spectral radius of $G$ is the largest eigenvalue of $M(G)$. In the present paper, we establish two graph perturbations with respect to ABC spectral radius. By applying these perturbations, the trees with the third, fourth, and fifth … WebAug 3, 2024 · The ABC matrix of a graph G, recently introduced by Estrada, is the square matrix of order G whose (i,j)-entry is equal to (di+dj−2)/(didj) if the i-th vertex and the j-th vertex of G are...

WebConsequently, the trees of order at least 10 with the 1st to 5th largest ABC spectral radii are determined. We wonder how the “Ruler Theorem” holds for ABC spectral radius of trees. Let G = ( V , E ) be a connected graph, where V = { v 1 , v 2 , … WebTwo graph perturbations with respect to ABC spectral radius are established. Consequently, the trees of order at least 10 with the 1st to 5th largest ABC spectral radii are determined. We wonder how the “Ruler Theorem” holds for ABC spectral radius of trees.

Weborder trees by their ABC spectral radii. The ordering results may indicate some research directions towards the answer of the question. In the present paper, we rstly investigate graph perturbations with respect to ABC spectral radius, and two non-trivial results are obtained. By applying the perturbations, we determine the trees with the third ...

WebWe show that the ordering of starlike trees by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. Spectral radius ordering of starlike trees: Linear and Multilinear Algebra: Vol 68, No 5 did mars have a magnetic fieldWebApr 20, 2024 · A supertree is a connected and acyclic hypergraph. For a hypergraph H, the maximal modulus of the eigenvalues of its adjacency tensor is called the spectral radius of H. By applying the operation of moving edges on hypergraphs and the weighted incidence matrix method, we determine the ninth and the tenth k-uniform supertrees with the largest … did marshawn lynch graduate from college did mars have a moonWebOn the spectral radii of trees, Journal of East China Normal University (Natural Science), 3: 22-28 (2004)] determined the ﬁrst seven trees of order n with the smallest spectral radius. In this paper, we extend this ordering by determining the trees with the eighth to the tenth smallest spectral radius among all trees withn vertices. did mars have tectonic platesWebJun 11, 2024 · Denote by Tn the set of trees on n vertices. Zhang and Li [X.D. Zang, J.S. Li, The two largest eigenvalues of Laplacian matrices of trees (in Chinese), J. China Univ. Sci. Technol. 28 (1998) 513518] and Guo [J.M. Guo, On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379385] give the first four trees in Tn , ordered according … did mars have an atmosphere like earthWebAug 3, 2024 · The ABC spectral radius of $G$ is the largest eigenvalue of $M(G)$. In the present paper, we establish two graph perturbations with respect to ABC spectral radius. By applying these perturbations, the trees with the third, fourth, and fifth largest ABC spectral radii are determined. did mars have life on itWebFeb 13, 2024 · It is concluded that the arithmetic-geometric spectral radius is a good indicator in forecasting Acentric Factor, Entropy and two topological descriptors SNar, HNar of octane isomers. Since molecular graphs of octane isomers are trees, we study arithmetic-geometric spectral radius of general trees. did mars have water and life