On the spectral radius of connected graphs
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 than 2; the A 0-spectral radii of H 5, H 6, H 7, H 8 and C … Web15 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…
On the spectral radius of connected graphs
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Web1 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 … http://ajc.maths.uq.edu.au/pdf/26/ajc_v26_p033.pdf
WebIn this paper, we completely characterize the (connected) graphs and (connected) triangle-free graphs which have the maximum, the minimum and second-minimum ABC … 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...
Web15 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 … 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 …
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
Web23 de jan. de 2011 · 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. For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the … imgy-f181-bWeb1 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. imgzone.shop.jd.comWeb6 de abr. de 2024 · The \(\alpha \)-spectral radius of a connected graph G is the spectral radius of \(A_\alpha \)-matrix of G.In this paper, we discuss the methods for comparing … list of premium rum brands with cigarsWeb6 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. list of preschool sight wordsWeb1 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... imgy-f181-b 口コミWeb6 de abr. de 2024 · 题目： The signless Laplacian spectral radius of graphs without intersecting odd cycles. 时间： 2024年4月10日（周一），14:45-16:30. 地点： 1C207. … img youth footballWeb1 de set. de 1988 · He showed that the spectral radius p (A) of A satisfies p (A) < ( - 1 + 1 + 8m )/2. Equality occurs if and only if m = ( 2 ) and G is a disjoint union of the complete … list of presbyterian hospitals in ghana