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.