Laplacian spectral moment and Laplacian Estrada index of random graphs

Nan Gao; Dan Hu; Xiaogang Liu; Shenggui Zhang

doi:10.1016/j.jmaa.2018.01.042

Laplacian spectral moment and Laplacian Estrada index of random graphs

Nan Gao
, Dan Hu
, Xiaogang Liu
, Shenggui Zhang

School of Mathematics and Statistics

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

2 Scopus citations

Abstract

Let G be a simple graph with n vertices and let μ₁≥μ₂≥⋯≥μ_n=0 be the Laplacian eigenvalues of G. The k-th Laplacian spectral moment of G is defined to be LM_k(G)=∑i=1nμ_i ^k(G), where k is a non-negative integer; and the Laplacian Estrada index of G is defined as LEE(G)=∑i=1ne^μ_i. In this paper, we first estimate these two indices for almost all graphs, and then we give lower and upper bounds to these two indices for almost all multipartite graphs.

Original language	English
Pages (from-to)	1299-1307
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	461
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.01.042
State	Published - 15 May 2018

Keywords

Erdős–Rényi random graph
Laplacian Estrada index
Laplacian spectral moment
Random multipartite graph

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10.1016/j.jmaa.2018.01.042

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title = "Laplacian spectral moment and Laplacian Estrada index of random graphs",

abstract = "Let G be a simple graph with n vertices and let μ1≥μ2≥⋯≥μn=0 be the Laplacian eigenvalues of G. The k-th Laplacian spectral moment of G is defined to be LMk(G)=∑i=1nμi k(G), where k is a non-negative integer; and the Laplacian Estrada index of G is defined as LEE(G)=∑i=1neμi . In this paper, we first estimate these two indices for almost all graphs, and then we give lower and upper bounds to these two indices for almost all multipartite graphs.",

keywords = "Erd{\H o}s–R{\'e}nyi random graph, Laplacian Estrada index, Laplacian spectral moment, Random multipartite graph",

author = "Nan Gao and Dan Hu and Xiaogang Liu and Shenggui Zhang",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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doi = "10.1016/j.jmaa.2018.01.042",

language = "英语",

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TY - JOUR

T1 - Laplacian spectral moment and Laplacian Estrada index of random graphs

AU - Gao, Nan

AU - Hu, Dan

AU - Liu, Xiaogang

AU - Zhang, Shenggui

PY - 2018/5/15

Y1 - 2018/5/15

N2 - Let G be a simple graph with n vertices and let μ1≥μ2≥⋯≥μn=0 be the Laplacian eigenvalues of G. The k-th Laplacian spectral moment of G is defined to be LMk(G)=∑i=1nμi k(G), where k is a non-negative integer; and the Laplacian Estrada index of G is defined as LEE(G)=∑i=1neμi . In this paper, we first estimate these two indices for almost all graphs, and then we give lower and upper bounds to these two indices for almost all multipartite graphs.

AB - Let G be a simple graph with n vertices and let μ1≥μ2≥⋯≥μn=0 be the Laplacian eigenvalues of G. The k-th Laplacian spectral moment of G is defined to be LMk(G)=∑i=1nμi k(G), where k is a non-negative integer; and the Laplacian Estrada index of G is defined as LEE(G)=∑i=1neμi . In this paper, we first estimate these two indices for almost all graphs, and then we give lower and upper bounds to these two indices for almost all multipartite graphs.

KW - Erdős–Rényi random graph

KW - Laplacian Estrada index

KW - Laplacian spectral moment

KW - Random multipartite graph

UR - https://www.scopus.com/pages/publications/85044337957

U2 - 10.1016/j.jmaa.2018.01.042

DO - 10.1016/j.jmaa.2018.01.042

M3 - 文章

AN - SCOPUS:85044337957

SN - 0022-247X

VL - 461

SP - 1299

EP - 1307

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Laplacian spectral moment and Laplacian Estrada index of random graphs

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