On Laplacian energy in terms of graph invariants

Kinkar Ch Das; Seyed Ahmad Mojallal; Ivan Gutman

doi:10.1016/j.amc.2015.06.064

On Laplacian energy in terms of graph invariants

Kinkar Ch Das, Seyed Ahmad Mojallal, Ivan Gutman

Department of Mathematics

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

28 Scopus citations

Abstract

Abstract For G being a graph with n vertices and m edges, and with Laplacian eigenvalues ^μ1≥^μ2≥⋯≥μn-₁≥^μn=0, the Laplacian energy is defined as LE=Σi=1n|^μi-2m/n|. Let σ be the largest positive integer such that μ_σ ≥ 2m/n. We characterize the graphs satisfying σ=n-1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.

Original language	English
Article number	21335
Pages (from-to)	83-92
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	268
DOIs	https://doi.org/10.1016/j.amc.2015.06.064
State	Published - 11 Jul 2015

Keywords

Edge connectivity
Laplacian eigenvalues
Laplacian energy
Spanning tree packing number
Vertex connectivity
Vertex cover number

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10.1016/j.amc.2015.06.064

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title = "On Laplacian energy in terms of graph invariants",

abstract = "Abstract For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ1≥μ2≥⋯≥μn-1≥μn=0, the Laplacian energy is defined as LE=Σi=1n|μi-2m/n|. Let σ be the largest positive integer such that μσ ≥ 2m/n. We characterize the graphs satisfying σ=n-1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.",

keywords = "Edge connectivity, Laplacian eigenvalues, Laplacian energy, Spanning tree packing number, Vertex connectivity, Vertex cover number",

author = "Das, \{Kinkar Ch\} and Mojallal, \{Seyed Ahmad\} and Ivan Gutman",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = jul,

day = "11",

doi = "10.1016/j.amc.2015.06.064",

language = "English",

volume = "268",

pages = "83--92",

journal = "Applied Mathematics and Computation",

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TY - JOUR

T1 - On Laplacian energy in terms of graph invariants

AU - Das, Kinkar Ch

AU - Mojallal, Seyed Ahmad

AU - Gutman, Ivan

PY - 2015/7/11

Y1 - 2015/7/11

N2 - Abstract For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ1≥μ2≥⋯≥μn-1≥μn=0, the Laplacian energy is defined as LE=Σi=1n|μi-2m/n|. Let σ be the largest positive integer such that μσ ≥ 2m/n. We characterize the graphs satisfying σ=n-1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.

AB - Abstract For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ1≥μ2≥⋯≥μn-1≥μn=0, the Laplacian energy is defined as LE=Σi=1n|μi-2m/n|. Let σ be the largest positive integer such that μσ ≥ 2m/n. We characterize the graphs satisfying σ=n-1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.

KW - Edge connectivity

KW - Laplacian eigenvalues

KW - Laplacian energy

KW - Spanning tree packing number

KW - Vertex connectivity

KW - Vertex cover number

UR - https://www.scopus.com/pages/publications/84936866762

U2 - 10.1016/j.amc.2015.06.064

DO - 10.1016/j.amc.2015.06.064

M3 - Article

AN - SCOPUS:84936866762

SN - 0096-3003

VL - 268

SP - 83

EP - 92

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 21335

ER -

On Laplacian energy in terms of graph invariants

Abstract

Keywords

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