On the second Laplacian spectral moment of a graph

Ying Liu; Yu Qin Sun

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 $(d_{1}, d_{2}, \dots, d_{n})$ , where $d_{1} \geq d_{2} \geq \dots \geq d_{n}$ . The spectral radius and the largest Laplacian eigenvalue are denoted by $ρ (G)$ and $μ (G)$ , respectively. We determine the graphs with $ρ (G) = \frac{d_{n} - 1}{2} + \sqrt{2 m - n d_{n} + \frac{{(d_{n} + 1)}^{2}}{4}}$ and the graphs with $d_{n} \geq 1$ and $μ (G) = d_{n} + \frac{1}{2} + \sqrt{\sum_{i = 1}^{n} d_{i} (d_{i} - d_{n}) + {(d_{n} - \frac{1}{2})}^{2}} .$ 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 $W_{n} = K_{1} \lor C_{n - 1}$ 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 $S (n, c, k)$ ( $c \geq 1$ , $k \geq 1$ ) 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 $c \geq 0$ and $k \geq 1$ .

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...

Bounds on Laplacian eigenvalues related to total and signed domination of graphs

Wei Shi, Liying Kang, Suichao Wu (2010)

Czechoslovak Mathematical Journal

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A total dominating set in a graph $G$ is a subset $X$ of $V (G)$ such that each vertex of $V (G)$ is adjacent to at least one vertex of $X$ . The total domination number of $G$ is the minimum cardinality of a total dominating set. A function $f : V (G) \to {- 1, 1}$ is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of $G$ is the minimum weight of an SDF on $G$ . In...