Note on Laplacian energy of graphs. (English) Zbl 1199.05217

Fath-Tabar, G. H.; Ashrafi, A. R.; Gutman, I.

Bull., Cl. Sci. Math. Nat., Sci. Math. 137, No. 33, 1-10 (2008).

Authors’ abstract: Let \(G\) be an \((n,m)\)-graph and \(\mu_1,\mu_2,\dots,\mu_n\) its Laplacian eigenvalues. The Laplacian energy \(LE\) of \(G\) is defined as \(\sum_{i=1}^n| \mu_i-2m/n| \). Some new bounds for \(LE\) are presented, and some results from the paper [B. Zhou and I. Gutman, “Nordhaus-Gaddum-type relations for the energy and Laplacian energy of graphs”, Bull., Cl. Sci. Math. Nat., Sci. Math. 134, No.32, 1-11 (2007; Zbl 1250.05074)] are improved and extended.

Reviewer: Dragoš Cvetković (Beograd)

MSC:

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.)

Keywords:

graph spectra; Laplacian eigenvalues; Laplacian energy

Citations:

Zbl 1250.05074