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Pirzada, S.; Ganie, Hilal A.
Linear algebra and its applications, 12/2015, Volume: 486Journal Article
Let G be a simple graph with n vertices, m edges, maximum degree Δ, average degree d‾=2mn, clique number ω having Laplacian eigenvalues μ1,μ2,…,μn−1,μn=0. For k (1≤k≤n), let Sk(G)=∑i=1kμi and let σ (1≤σ≤n−1) be the number of Laplacian eigenvalues greater than or equal to average degree d‾. In this paper, we obtain a lower bound for Sω−1(G) and an upper bound for Sσ(G) in terms of m, Δ, σ and clique number ω of the graph. As an application, we obtain the stronger bounds for the Laplacian energy LE(G)=∑i=1n|μi−d‾|, which improve some well known earlier bounds.
