On the spectral radius of connected graphs

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August undefined, 2024

WebLet G = (V, E) be a finite undirected graph of order n and of size m.Let Δ and δ be the largest and the smallest degree of G, respectively.The spectral radius of G is the … Web6 de abr. de 2024 · In this paper, we discuss the methods for comparing \ (\alpha \)-spectral radius of graphs. As applications, we characterize the graphs with the maximal \ (\alpha \)-spectral radius...

On the distance Laplacian spectral radius of bicyclic graphs

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 linear combinations S α ( G) = α D ( G) + ( 1 − α) A ( G) where α ∈ [ 0, 1]. Let ρ ( S α ( G)) be the spectral radius of S α ( G). Web1 de jan. de 2005 · Liu et al. [8] showed that K k n is the unique graph having the largest spectral radius in all the connected graphs with n vertices and k cut edges, where K k n is a graph obtained by... poly mud flaps

On Zagreb index, signless Laplacian eigenvalues and signless

Web1 de ago. de 2024 · The spectral radius of a graph sometimes can give some information about the structure of graphs. For example, it is well-known [4, p. 34] that the average … 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 distance matrix of G. The la... Web1 de nov. de 2012 · A cactus is a connected graph in which any two cycles have at most one common vertex. In this article, we determine the unique graph with minimal distance spectral radius in the class of... shank toothbrush

The signless Laplacian spectral radius of graphs without …

Some spectral inequalities for connected bipartite graphs with …

Web11 de abr. de 2024 · Let G be a connected graph on n vertices with e(G) distinct Q-eigenvalues. Then $e(G)=2$ ... Ning W, Li H, Lu M (2013) On the signless Laplacian spectral radius of irregular graphs. Linear Algebra Appl 438:2280–2288. Article MathSciNet MATH Google Scholar Pirzada S (2012) An introduction to graph theory. Web15 de jul. de 2024 · The Aα- spectral radius of Gis the largest eigenvalue of Aα(G). In this paper, we determine the first three largest extremal graphs in Halin graphs by their Aα- spectral radii when 12≤α<1. For 0≤α≤1, the 3-regular Halin graph alone minimizes the Aα- spectral radius for Halin graphs. Previousarticlein issue Nextarticlein issue MSC 05C50 … shank trading companyWeb1 de ago. de 2004 · On the spectral radius of graphs. ☆. Let G be a simple undirected graph. For v ∈ V ( G ), the 2-degree of v is the sum of the degrees of the vertices … shank traducere

"WebBefore giving the proof of Theorem1.2, we list all connected graphs with A 0-spectral radius at most 2 (see [10]): the A 0-spectral radii of H 1, H 2, H 3, H 4 and P n are less … " - On the spectral radius of connected graphs

On the spectral radius of connected graphs

$[PDF] On the $A_\alpha$-spectral radius of graphs without linear ...$

Web1 de ago. de 2024 · For a connected graph G on k ≥ 2 vertices, by Perron-Frobenius theorem, the spectral radius ρ ( G) of A ( G) is a simple positive eigenvalue and the associated eigenvector is entry-wise positive (for details see [1]). We will refer to such an eigenvector as the Perron vector of G. Web21 de abr. de 2024 · A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted. In this …

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Web10 de jan. de 2024 · [Show full abstract] bounds for the distance α-spectral radius, especially for graphs that are not transmission regular, propose local graft … WebWe give upper bounds for -spectral radius for unicyclic graphs Gwith maximum degree 2, connected irregular graphs with given max-imum degree and and some other graph parameters, and graphs with given domination number, respectively. We determine the unique tree with second maximum -spectral radius among trees, and the unique tree …

Web1 de mar. de 2024 · Let G be a simple graph of order n and also let ρ (G) be the spectral radius of the graph G. In this paper, we prove that ρ (G) ≤ ρ 2 (G − v k) + 2 d k − 1 for … Webspectral radius have attracted many interests among the mathematical literature including linear algebra and graph theory. An interesting problem in the spectral graph theory is …

WebOn Distance Spectral Radius and Distance Energy of Graphs. Bo Zhou, Aleksandar Ilić. Mathematics, Computer Science. 2010. TLDR. Lower and upper bounds for the distance spectral radius of graphs and bipartite graphs, lower bounds forThe distance energy of graphs, and characterize the extremal graphs are established. 79. Web1 de out. de 2024 · In this paper, we determine the graph having the maximum A α-spectral radius for α ∈ [1 2, 1) among all connected graphs of size m and diameter (at least) d. …

WebIn this note, we obtain two lower bounds for the spectral radius λ1(L(G)) of triangle-free graphs; one is in terms of the numbers of edges and vertices of graphs, and the other is in terms of degrees and average 2-degrees of vertices. We also obtain some other related results. For triangle-free graphs, the second bound is better than

Web15 de abr. de 2007 · Some sharp bounds are obtained for the (Laplacian) spectral radii of connected graphs. As consequences, some (sharp) upper bounds of the Nordhaus–Gaddum type are also obtained for the sum of (Laplacian) spectral radii of a connected graph and its connected complement. AMS classification 05C50 15A42 … shank townWeb15 de fev. de 2024 · The spectral radius of G, denoted by ρ (G), is the largest eigenvalue of A (G). When G is connected, A (G) is irreducible and by the Perron-Frobenius … shank traduccionWebarXiv:2206.07872v1 [math.CO] 16 Jun 2024 On the spectral radius of minimally 2-(edge)-connected graphs with given size* Zhenzhen Loua, Gao Mina, Qiongxiang Huanga† aCollege of Mathematics and Systems Science, Xinjiang University,Urumqi, Xinjiang … shank trainer pcWeb6 de abr. de 2024 · As early as 1985, Brualdi and Hoffman Brualdi and Hoffman ( 1985) investigated the maximal spectral radius of the adjacency matrix of a graph in the set of all graphs with a given number of vertices and edges. Their work was followed by other people, in the connected graph case as well as in the general case. shank train stageWebOn the spectral radius of minimally 2- (edge)-connected graphs with given size. Lou, Zhenzhen. ; Gao, Min. ; Huang, Qiongxiang. A graph is minimally k -connected ( k … shank traductionWeb15 de dez. de 2024 · On the Aα-spectral radius of connected graphs A. Alhevaz, M. Baghipur, H. A. Ganie, K. Das Mathematics Ars Mathematica Contemporanea 2024 For a simple graph G , the generalized adjacency matrix A α ( G ) is defined as A α ( G ) = αD ( G ) + (1 − α ) A ( G ) , α ∈ [0 , 1] , where A ( G ) is the adjacency matrix and D ( G ) is the… shank trainerWebHá 1 dia · The minimal spectral radius with given independence number. Jinwon Choi, Jooyeon Park. In this paper, we determine the graphs which have the minimal spectral … polymumps accelerometer