Comparison between Kirchhoff index and the Laplacian-energy-like invariant
| Autor: | Kexiang Xu, Ivan Gutman, Kinkar Ch. Das |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Numerical Analysis Laplacian spectrum (of graph) Algebra and Number Theory Laplacian-energy-like invariant 0211 other engineering and technologies Kirchhoff index 021107 urban & regional planning 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Laplacian eigenvalues LEL Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Invariant (mathematics) Laplacian matrix Laplace operator Connectivity Graph spectrum Mathematics |
| Zdroj: | Linear Algebra and its Applications. 436(9):3661-3671 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2012.01.002 |
| Popis: | Let G be a connected graph of order n with Laplacian eigenvalues μ 1 ⩾ μ 2 ⩾ ⋯ ⩾ μ n - 1 > μ n = 0 . The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as Kf = n ∑ k = 1 n - 1 1 / μ k and LEL = ∑ k = 1 n - 1 μ k , respectively. We compare Kf and LEL and establish two sufficient conditions under which LEL Kf . The connected graphs of order n with nine greatest Kirchhoff indices are determined; for these LEL > Kf holds. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect