Sharp upper bounds on the spectral radius of the Laplacian matrix of graphs.

Das, K.Ch.

Displaying similar documents to “Sharp upper bounds on the spectral radius of the Laplacian matrix of graphs.”

The spectral radius and the maximum degree of irregular graphs.

Cioabă, Sebastian M. (2007)

The Electronic Journal of Combinatorics [electronic only]

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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.

Spectral characterization of multicone graphs

Jianfeng Wang, Haixing Zhao, Qiongxiang Huang (2012)

Czechoslovak Mathematical Journal

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A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho's result [B. Zhou, H. H. Cho, Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 (130) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph....