Displaying similar documents to “Some properties of the distance Laplacian eigenvalues of a graph”

Some graphs determined by their (signless) Laplacian spectra

Muhuo Liu (2012)

Czechoslovak Mathematical Journal

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Let W n = K 1 ∨ C n - 1 be the wheel graph on n vertices, and let S ( n , c , k ) be the graph on n vertices obtained by attaching n - 2 c - 2 k - 1 pendant edges together with k hanging paths of length two at vertex v 0 , where v 0 is the unique common vertex of c triangles. In this paper we show that S ( n , c , k ) ( c ≥ 1 , k ≥ 1 ) and W n are determined by their signless Laplacian spectra, respectively. Moreover, we also prove that S ( n , c , k ) and its complement graph are determined by their Laplacian spectra, respectively, for c ≥ 0 and k ≥ 1 .

On the sum of powers of Laplacian eigenvalues of bipartite graphs

Bo Zhou, Aleksandar Ilić (2010)

Czechoslovak Mathematical Journal

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For a bipartite graph G and a non-zero real α , we give bounds for the sum of the α th powers of the Laplacian eigenvalues of G using the sum of the squares of degrees, from which lower and upper bounds for the incidence energy, and lower bounds for the Kirchhoff index and the Laplacian Estrada index are deduced.

Algebraic conditions for t -tough graphs

Bo Lian Liu, Siyuan Chen (2010)

Czechoslovak Mathematical Journal

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We give some algebraic conditions for t -tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.

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.