共查询到20条相似文献,搜索用时 15 毫秒
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We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained. 相似文献
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Let us consider weighted graphs, where the weights of the edges are positive definite matrices. The eigenvalues of a weighted graph are the eigenvalues of its adjacency matrix and the spectral radius of a weighted graph is also the spectral radius of its adjacency matrix. In this paper, we obtain two upper bounds for the spectral radius of weighted graphs and compare with a known upper bound. We also characterize graphs for which the upper bounds are attained. 相似文献
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Kinkar Ch. Das 《Applied mathematics and computation》2011,217(18):7420-7426
We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained. 相似文献
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Fernando Garibay Bonales Rigoberto Vera Mendoza 《Proceedings of the American Mathematical Society》1998,126(1):97-103
In a Banach space, Gelfand's formula is used to find the spectral radius of a continuous linear operator. In this paper, we show another way to find the spectral radius of a bounded linear operator in a complete topological linear space. We also show that Gelfand's formula holds in a more general setting if we generalize the definition of the norm for a bounded linear operator.
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Bolian Liu 《Discrete Mathematics》2008,308(23):5317-5324
We give some upper bounds for the spectral radius of bipartite graph and graph, which improve the result in Hong’s Paper [Y. Hong, J.-L. Shu, K. Fang, A sharp upper bound of the spectral radius of graphs, J. Combin. Theory Ser. B 81 (2001) 177-183]. 相似文献
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A. Dilek Güngör 《Applied mathematics and computation》2010,216(3):791-799
Let G be a digraph with n vertices and m arcs without loops and multiarcs. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, sharp upper and lower bounds on ρ(G) are given. We show that some known bounds can be obtained from our bounds. 相似文献
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In this paper, we discuss the spectral radius of nonnegative centrosymmetric matrices. By using the centrosymmetric structure, we establish some estimations of the spectral radius. 相似文献
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On the spectral radius of unicyclic graphs with fixed diameter 总被引:1,自引:0,他引:1
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Let be a weighted digraph with vertex set and arc set , where the arc weights are nonzero nonnegative symmetric matrices. In this paper, we obtain an upper bound on the signless Laplacian spectral radius of a weighted digraph , and if is strongly connected, we also characterize the digraphs achieving the upper bound. Moreover, we show that an upper bound of weighted digraphs or unweighted digraphs can be deduced from our upper bound. 相似文献
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Harald K. Wimmer 《Journal of Mathematical Analysis and Applications》2011,381(1):80-86
In this paper we study a class of matrix polynomials with the property that spectral radius and numerical radius coincide. Special attention is paid to the spectrum on the boundary of the numerical range. 相似文献
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Shang-wang Tan 《Discrete Mathematics》2010,310(5):1026-1212
The spectrum of weighted graphs is often used to solve the problems in the design of networks and electronic circuits. We first give some perturbational results on the (signless) Laplacian spectral radius of weighted graphs when some weights of edges are modified; we then determine the weighted tree with the largest Laplacian spectral radius in the set of all weighted trees with a fixed number of pendant vertices and a positive weight set. Furthermore, we also derive the weighted trees with the largest Laplacian spectral radius in the set of all weighted trees with a fixed positive weight set and independence number, matching number or total independence number. 相似文献
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The spectra of weighted graphs are given attention by some authors because the graphs in the design of networks and electronic circuits are usually weighted. In this short paper, we completely determine the spectra of weighted double stars. We also give the weighted double star that achieves the maximal spectral radius. 相似文献
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A bicyclic graph is a connected graph in which the number of edges equals the number of vertices plus one. Let Δ(G) and ρ(G) denote the maximum degree and the spectral radius of a graph G, respectively. Let B(n) be the set of bicyclic graphs on n vertices, and B(n,Δ)={G∈B(n)∣Δ(G)=Δ}. When Δ≥(n+3)/2 we characterize the graph which alone maximizes the spectral radius among all the graphs in B(n,Δ). It is also proved that for two graphs G1 and G2 in B(n), if Δ(G1)>Δ(G2) and Δ(G1)≥⌈7n/9⌉+9, then ρ(G1)>ρ(G2). 相似文献
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Urszula Ostaszewska 《Journal of Mathematical Analysis and Applications》2010,361(1):246-251
In this paper we derive a relationship between the Legendre-Fenchel transform of the spectral exponent of weighted composition operators acting in Lp-spaces and the Legendre-Fenchel transform obtained for their polynomials. We establish the variational principle for the spectral exponent of polynomials of weighted composition operators. 相似文献
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Examples show that many integral forms can be efficiently verified to be positive through a special form of variable substitutions, i.e., weighted difference substitutions (WDS), but it was unknown how many steps of substitutions are needed, or furthermore, whether this method is adapted for checking positivity of all integral forms. In this paper, we give upper bounds of step numbers of WDS required in checking whether an integral form is positive or nonnegative, thus deducing that the positivity of integral forms can be completely verified through the WDS method. 相似文献
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Let be a simple connected graph with vertices and edges. The spectral radius of is the largest eigenvalue of its adjacency matrix. In this paper, we firstly consider the effect on the spectral radius of a graph by removing a vertex, and then as an application of the result, we obtain a new sharp upper bound of which improves some known bounds: If , where is an integer, then The equality holds if and only if is a complete graph or , where is the graph obtained from by deleting some edge . 相似文献