Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions

Jia Bao Liu; Jinde Cao; Tasawar Hayat; Fuad E. Alsaadi

doi:10.1186/s40064-016-3028-1

Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions

Jia Bao Liu
, Jinde Cao
, Tasawar Hayat
, Fuad E. Alsaadi

Anhui Jianzhu University
Southeast University, Nanjing
Faculty of Sciences, King Abdulaziz University

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

1 Scopus citations

Abstract

Let G be a connected graph of order n with Laplacian eigenvalues μ₁(G) ≥ μ₂(G) ≥ ⋯ ≥ μ_n(G) = 0. The Laplacian-energy-like invariant of G, is defined as LEL(G)=∑i=1n-1μi. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that M^t(n, m) , M^c(n, m) and M^f(n, m) have the same asymptotic Laplacian-energy-like invariants.

Original language	English
Article number	1415
Journal	SpringerPlus
Volume	5
Issue number	1
DOIs	https://doi.org/10.1186/s40064-016-3028-1
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Laplacian spectrum
Laplacian-energy-like invariant
Lattice
Toroidal lattice

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10.1186/s40064-016-3028-1

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title = "Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions",

abstract = "Let G be a connected graph of order n with Laplacian eigenvalues μ1(G) ≥ μ2(G) ≥ ⋯ ≥ μn(G) = 0. The Laplacian-energy-like invariant of G, is defined as LEL(G)=∑i=1n-1μi. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that Mt(n, m) , Mc(n, m) and Mf(n, m) have the same asymptotic Laplacian-energy-like invariants.",

keywords = "Laplacian spectrum, Laplacian-energy-like invariant, Lattice, Toroidal lattice",

author = "Liu, \{Jia Bao\} and Jinde Cao and Tasawar Hayat and Alsaadi, \{Fuad E.\}",

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T1 - Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions

AU - Liu, Jia Bao

AU - Cao, Jinde

AU - Hayat, Tasawar

AU - Alsaadi, Fuad E.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let G be a connected graph of order n with Laplacian eigenvalues μ1(G) ≥ μ2(G) ≥ ⋯ ≥ μn(G) = 0. The Laplacian-energy-like invariant of G, is defined as LEL(G)=∑i=1n-1μi. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that Mt(n, m) , Mc(n, m) and Mf(n, m) have the same asymptotic Laplacian-energy-like invariants.

AB - Let G be a connected graph of order n with Laplacian eigenvalues μ1(G) ≥ μ2(G) ≥ ⋯ ≥ μn(G) = 0. The Laplacian-energy-like invariant of G, is defined as LEL(G)=∑i=1n-1μi. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that Mt(n, m) , Mc(n, m) and Mf(n, m) have the same asymptotic Laplacian-energy-like invariants.

KW - Laplacian spectrum

KW - Laplacian-energy-like invariant

KW - Lattice

KW - Toroidal lattice

UR - https://www.scopus.com/pages/publications/84983542343

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DO - 10.1186/s40064-016-3028-1

M3 - Article

AN - SCOPUS:84983542343

SN - 2193-1801

VL - 5

JO - SpringerPlus

JF - SpringerPlus

IS - 1

M1 - 1415

ER -

Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions

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