Comparison between Kirchhoff index and the Laplacian-energy-like invariant

Kinkar Ch Das; Kexiang Xu; Ivan Gutman

doi:10.1016/j.laa.2012.01.002

Comparison between Kirchhoff index and the Laplacian-energy-like invariant

Kinkar Ch Das, Kexiang Xu, Ivan Gutman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

Let G be a connected graph of order n with Laplacian eigenvalues ^μ1≥ ^μ2≥⋯≥μn- ₁> ^μn=0. The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as Kf=n∑k=1n-11/ ^μk and LEL=∑k=1n-1 ^μk, 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.

Original language	English
Pages (from-to)	3661-3671
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	436
Issue number	9
DOIs	https://doi.org/10.1016/j.laa.2012.01.002
State	Published - 1 May 2012

Keywords

Graph spectrum
Kirchhoff index
Laplacian spectrum (of graph)
Laplacian-energy-like invariant
LEL

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10.1016/j.laa.2012.01.002

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title = "Comparison between Kirchhoff index and the Laplacian-energy-like invariant",

abstract = "Let G be a connected graph of order n with Laplacian eigenvalues μ1≥ μ2≥⋯≥μn- 1> μn=0. The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as Kf=n∑k=1n-11/ μk and LEL=∑k=1n-1 μk, respectively. We compare Kf and LEL and establish two sufficient conditions under which LELKf holds.",

keywords = "Graph spectrum, Kirchhoff index, Laplacian spectrum (of graph), Laplacian-energy-like invariant, LEL",

author = "Das, \{Kinkar Ch\} and Kexiang Xu and Ivan Gutman",

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T1 - Comparison between Kirchhoff index and the Laplacian-energy-like invariant

AU - Das, Kinkar Ch

AU - Xu, Kexiang

AU - Gutman, Ivan

PY - 2012/5/1

Y1 - 2012/5/1

N2 - Let G be a connected graph of order n with Laplacian eigenvalues μ1≥ μ2≥⋯≥μn- 1> μn=0. The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as Kf=n∑k=1n-11/ μk and LEL=∑k=1n-1 μk, respectively. We compare Kf and LEL and establish two sufficient conditions under which LELKf holds.

AB - Let G be a connected graph of order n with Laplacian eigenvalues μ1≥ μ2≥⋯≥μn- 1> μn=0. The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as Kf=n∑k=1n-11/ μk and LEL=∑k=1n-1 μk, respectively. We compare Kf and LEL and establish two sufficient conditions under which LELKf holds.

KW - Graph spectrum

KW - Kirchhoff index

KW - Laplacian spectrum (of graph)

KW - Laplacian-energy-like invariant

KW - LEL

UR - https://www.scopus.com/pages/publications/84858000648

U2 - 10.1016/j.laa.2012.01.002

DO - 10.1016/j.laa.2012.01.002

M3 - Article

AN - SCOPUS:84858000648

SN - 0024-3795

VL - 436

SP - 3661

EP - 3671

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 9

ER -

Comparison between Kirchhoff index and the Laplacian-energy-like invariant

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Keywords

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