A Note on the Bounds of Laplacian-energy-like-invariant

Document Type : Research Paper


1 payame noor university

2 Inviting lecturer of Iran university of science and technology


The Laplacian-energy-like of a simple connected graph G is defined as
LEL:=LEL(G)=∑_(i=1)^n√(μ_i ),
Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the number of triangles in graph.


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