Displaying similar documents to “On the sum of powers of Laplacian eigenvalues of bipartite graphs”

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...

On the second Laplacian spectral moment of a graph

Ying Liu, Yu Qin Sun (2010)

Czechoslovak Mathematical Journal

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Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. () (2006), 1207–1213) gave the definition of Laplacian energy of a graph G and proved L E ( G ) ≥ 6 n - 8 ; equality holds if and only if G = P n . In this paper we consider the relation between the Laplacian energy and the chromatic number of a graph G and give an upper bound for the Laplacian energy on a connected graph.

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.