Displaying similar documents to “On a bound on algebraic connectivity: the case of equality”

Constructions for type I trees with nonisomorphic Perron branches

Stephen J. Kirkland (1999)

Czechoslovak Mathematical Journal

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A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections...

Bounds on the subdominant eigenvalue involving group inverses with applications to graphs

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

Czechoslovak Mathematical Journal

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Let A be an n × n symmetric, irreducible, and nonnegative matrix whose eigenvalues are λ 1 > λ 2 ... λ n . In this paper we derive several lower and upper bounds, in particular on λ 2 and λ n , but also, indirectly, on μ = max 2 i n | λ i | . The bounds are in terms of the diagonal entries of the group generalized inverse, Q # , of the singular and irreducible M-matrix Q = λ 1 I - A . Our starting point is a spectral resolution for Q # . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity...

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.