Displaying similar documents to “Some properties of Laplacian eigenvectors.”

Some properties of the distance Laplacian eigenvalues of a graph

Mustapha Aouchiche, Pierre Hansen (2014)

Czechoslovak Mathematical Journal

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The distance Laplacian of a connected graph G is defined by ℒ = Diag ( Tr ) - 𝒟 , where 𝒟 is the distance matrix of G , and Diag ( Tr ) is the diagonal matrix whose main entries are the vertex transmissions in G . The spectrum of ℒ is called the distance Laplacian spectrum of G . In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties...

Eigenvalue Conditions for Induced Subgraphs

Jochen Harant, Julia Niebling, Sebastian Richter (2015)

Discussiones Mathematicae Graph Theory

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Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.

The Laplacian spread of graphs

Zhifu You, Bo Lian Liu (2012)

Czechoslovak Mathematical Journal

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The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected c -cyclic graphs with n vertices and Laplacian spread n - 1 are discussed.