Please use this identifier to cite or link to this item:
https://scidar.kg.ac.rs/handle/123456789/11104
Title: | On Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs |
Authors: | das, kinkar Gutman, Ivan |
Issue Date: | 2018 |
Abstract: | © 2018 Elsevier Inc. Let G be a connected graph of order n and size m with Laplacian eigenvalues μ1≥μ2≥⋯≥μn=0. The Kirchhoff index of G, denoted by Kf, is defined as: Kf=n∑i=1n−1[Formula presented]. The Laplacian-energy-like invariant (LEL) and the Laplacian energy (LE) of the graph G, are defined as: LEL=∑i=1n−1μi and LE=∑i=1n|μi−[Formula presented]|, respectively. We obtain two relations on LEL with Kf, and LE with Kf. For two classes of graphs, we prove that LEL>Kf. Finally, we present an upper bound on the ratio LE/LEL and characterize the extremal graphs. |
URI: | https://scidar.kg.ac.rs/handle/123456789/11104 |
Type: | article |
DOI: | 10.1016/j.laa.2018.05.030 |
ISSN: | 0024-3795 |
SCOPUS: | 2-s2.0-85047946407 |
Appears in Collections: | Faculty of Science, Kragujevac |
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