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Displaying similar documents to “Improved upper bounds for the Laplacian spectral radius 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.

An upper bound on the Laplacian spectral radius of the signed graphs

Hong-Hai Li, Jiong-Sheng Li (2008)

Discussiones Mathematicae Graph Theory

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In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

Sharp Upper Bounds on the Clar Number of Fullerene Graphs

Yang Gao, Heping Zhang (2018)

Discussiones Mathematicae Graph Theory

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The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices n ≥ 20 except n = 22 and n = 30.