On the spectral radius of connected graphs
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... 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 …
On the spectral radius of connected graphs
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Web1 de abr. de 2024 · O [12] obtained a sharp lower bound of the spectral radius of a connected graph G to guarantee that G has a perfect matching. Very recently, Kim et … 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...
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… Web1 de ago. de 2024 · One can easily see that the A α -spectral radius is strictly increasing if adding an edge for a connected graph. If N P ( v) ≤ 2, then we can add an edge …
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 … 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 …
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...
Web5 de abr. de 2024 · As well known, the spectral radius is not larger than the maximum degree in a graph. It is interesting to study the difference between maximum degree and spectral radius in an irregular graph. Let G be a connected irregular graph on n vertices and m edges, and with maximum degree \Delta, minimum degree \delta and diameter D. how do you insert a check mark in wordWebIn 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 phone app for computer uploadsWeb23 de mai. de 2024 · On the [Math Processing Error] spectral radius of strongly connected digraphs Weige Xi, Ligong Wang Let [Math Processing Error] be a digraph with adjacency matrix [Math Processing Error]. Let [Math Processing Error] be the diagonal matrix with outdegrees of vertices of [Math Processing Error]. how do you insert a check mark in excelhttp://ajc.maths.uq.edu.au/pdf/26/ajc_v26_p033.pdf how do you input a drop down list in excelWebOn 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. how do you insert a catheterWeb16 de jun. de 2024 · Naturally, for a fixed size of a minimally $k$-(edge)-connected graphs, what is the extremal spectral radius? In this paper, we determine the maximum spectral … phone app for covid vaccine registrationWeb6 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... how do you insert a checkmark in word