Displaying similar documents to “Graphs with given degree sequence and maximal spectral radius.”

The first Dirichlet eigenvalue of bicyclic graphs

Guang-Jun Zhang, Xiao-Dong Zhang (2012)

Czechoslovak Mathematical Journal

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In this paper, we have investigated some properties of the first Dirichlet eigenvalue of a bicyclic graph with boundary condition. These results can be used to characterize the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicyclic graphs with a given graphic bicyclic degree sequence with minor conditions. Moreover, the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicycle graphs with fixed k interior vertices...

On the multiplicity of Laplacian eigenvalues of graphs

Ji-Ming Guo, Lin Feng, Jiong-Ming Zhang (2010)

Czechoslovak Mathematical Journal

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In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.