Displaying similar documents to “The third smallest eigenvalue of the Laplacian matrix.”

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.

On a bound on algebraic connectivity: the case of equality

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

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In a recent paper the authors proposed a lower bound on 1 - λ i , where λ i , λ i ≠ 1 , is an eigenvalue of a transition matrix T of an ergodic Markov chain. The bound, which involved the group inverse of I - T , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in...