Upper bounds for the sum of Laplacian eigenvalues of graphs |
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Authors: | Zhibin Du Bo Zhou |
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Affiliation: | 1. Department of Mathematics, Tongji University, Shanghai 200092, PR China;2. Department of Mathematics, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | Let G be a graph with n vertices and edges, and let be the Laplacian eigenvalues of G. Let , where . Brouwer conjectured that for . It has been shown in Haemers et al. [7] that the conjecture is true for trees. We give upper bounds for , and in particular, we show that the conjecture is true for unicyclic and bicyclic graphs. |
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