Energy of generalized line graphs

Weiwei Lang; Ligong Wang

doi:10.1016/j.laa.2012.05.023

Energy of generalized line graphs

Weiwei Lang, Ligong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

5 Scopus citations

Abstract

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Line graphs play an important role in the study of graph theory. Generalized line graphs extend the ideas of both line graphs and cocktail party graphs. In this paper, we establish relations between the energy of the generalized line graph of a graph G and the Laplacian and signless Laplacian energies of G. We give upper and lower bounds for the energy of generalized line graphs. Finally, we present upper and lower bounds for some special graphs.

Original language	English
Pages (from-to)	2386-2396
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	437
Issue number	9
DOIs	https://doi.org/10.1016/j.laa.2012.05.023
State	Published - 1 Nov 2012

Keywords

Energy
Generalized line graphs
Laplacian energy
Signless Laplacian energy

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10.1016/j.laa.2012.05.023

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abstract = "The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Line graphs play an important role in the study of graph theory. Generalized line graphs extend the ideas of both line graphs and cocktail party graphs. In this paper, we establish relations between the energy of the generalized line graph of a graph G and the Laplacian and signless Laplacian energies of G. We give upper and lower bounds for the energy of generalized line graphs. Finally, we present upper and lower bounds for some special graphs.",

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AB - The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Line graphs play an important role in the study of graph theory. Generalized line graphs extend the ideas of both line graphs and cocktail party graphs. In this paper, we establish relations between the energy of the generalized line graph of a graph G and the Laplacian and signless Laplacian energies of G. We give upper and lower bounds for the energy of generalized line graphs. Finally, we present upper and lower bounds for some special graphs.

KW - Energy

KW - Generalized line graphs

KW - Laplacian energy

KW - Signless Laplacian energy

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VL - 437

SP - 2386

EP - 2396

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 9

ER -

Energy of generalized line graphs

Abstract

Keywords

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