Maximum Laplacian energy of unicyclic graphs

Kinkar Ch Das; Eliseu Fritscher; Lucélia Kowalski Pinheiro; Vilmar Trevisan

doi:10.1016/j.dam.2016.10.023

Maximum Laplacian energy of unicyclic graphs

Kinkar Ch Das, Eliseu Fritscher, Lucélia Kowalski Pinheiro, Vilmar Trevisan

Department of Mathematics

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

11 Scopus citations

Abstract

We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs, obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic graph on n vertices having largest (signless) Laplacian energy for 3≤n≤13. For n≥11, we conjecture that the graph consisting of a triangle together with n−3 balanced distributed pendent vertices is the candidate having the maximum (signless) Laplacian energy among connected unicyclic graphs on n vertices. We prove this conjecture for many classes of graphs, depending on σ, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.

Original language	English
Pages (from-to)	71-81
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	218
DOIs	https://doi.org/10.1016/j.dam.2016.10.023
State	Published - 19 Feb 2017

Keywords

Laplacian energy
Laplacian matrix
Signless Laplacian energy
Unicyclic graph

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10.1016/j.dam.2016.10.023

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title = "Maximum Laplacian energy of unicyclic graphs",

abstract = "We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs, obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic graph on n vertices having largest (signless) Laplacian energy for 3≤n≤13. For n≥11, we conjecture that the graph consisting of a triangle together with n−3 balanced distributed pendent vertices is the candidate having the maximum (signless) Laplacian energy among connected unicyclic graphs on n vertices. We prove this conjecture for many classes of graphs, depending on σ, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.",

keywords = "Laplacian energy, Laplacian matrix, Signless Laplacian energy, Unicyclic graph",

author = "Das, \{Kinkar Ch\} and Eliseu Fritscher and Pinheiro, \{Luc{\'e}lia Kowalski\} and Vilmar Trevisan",

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year = "2017",

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doi = "10.1016/j.dam.2016.10.023",

language = "English",

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T1 - Maximum Laplacian energy of unicyclic graphs

AU - Das, Kinkar Ch

AU - Fritscher, Eliseu

AU - Pinheiro, Lucélia Kowalski

AU - Trevisan, Vilmar

PY - 2017/2/19

Y1 - 2017/2/19

N2 - We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs, obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic graph on n vertices having largest (signless) Laplacian energy for 3≤n≤13. For n≥11, we conjecture that the graph consisting of a triangle together with n−3 balanced distributed pendent vertices is the candidate having the maximum (signless) Laplacian energy among connected unicyclic graphs on n vertices. We prove this conjecture for many classes of graphs, depending on σ, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.

AB - We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs, obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic graph on n vertices having largest (signless) Laplacian energy for 3≤n≤13. For n≥11, we conjecture that the graph consisting of a triangle together with n−3 balanced distributed pendent vertices is the candidate having the maximum (signless) Laplacian energy among connected unicyclic graphs on n vertices. We prove this conjecture for many classes of graphs, depending on σ, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.

KW - Laplacian energy

KW - Laplacian matrix

KW - Signless Laplacian energy

KW - Unicyclic graph

UR - https://www.scopus.com/pages/publications/85007382364

U2 - 10.1016/j.dam.2016.10.023

DO - 10.1016/j.dam.2016.10.023

M3 - Article

AN - SCOPUS:85007382364

SN - 0166-218X

VL - 218

SP - 71

EP - 81

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Maximum Laplacian energy of unicyclic graphs

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Keywords

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