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- W1971651113 abstract "Let G be a simple graph with n vertices and e ( G ) edges. Brouwer et al. conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e ( G ) + k + 1 2 , where 1 ≤ k ≤ n . In this paper, this conjecture is proved to be true for the following cases: connected graphs with sufficiently large k , unicyclic graphs, bicyclic graphs and tricyclic graphs with some restrictions, forests, etc. Moreover, we show that if G is a tree with a specified property, then the sum of the k largest Laplacian eigenvalues of G is at most e ( G ) + 2 k − 2 , where 1 ≤ k ≤ n ." @default.
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- W1971651113 date "2012-08-01" @default.
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- W1971651113 title "On a conjecture for the sum of Laplacian eigenvalues" @default.
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- W1971651113 doi "https://doi.org/10.1016/j.mcm.2011.12.047" @default.
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