Geodesic
The Laplacian spread of graphs
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 155-168 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-012-0003-z
Classification : 05C50, 15A18
Keywords: Laplacian eigenvalues; spread 
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You, Zhifu; Liu, BoLian. The Laplacian spread of graphs. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 155-168. doi: 10.1007/s10587-012-0003-z

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