Displaying similar documents to “On the second Laplacian spectral moment of a graph”

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.

Remarks on spectral radius and Laplacian eigenvalues of a graph

Bo Zhou, Han Hyuk Cho (2005)

Czechoslovak Mathematical Journal

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Let G be a graph with n vertices, m edges and a vertex degree sequence ( d 1 , d 2 , , d n ) , where d 1 d 2 d n . The spectral radius and the largest Laplacian eigenvalue are denoted by ρ ( G ) and μ ( G ) , respectively. We determine the graphs with ρ ( G ) = d n - 1 2 + 2 m - n d n + ( d n + 1 ) 2 4 and the graphs with d n 1 and μ ( G ) = d n + 1 2 + i = 1 n d i ( d i - d n ) + d n - 1 2 2 . We also present some sharp lower bounds for the Laplacian eigenvalues of a connected 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 .