Coulson-type integral formulas for the general energy of a vertex

Lu Qiao; Shenggui Zhang; Jing Li; Nan Gao

doi:10.1016/j.jmaa.2022.126565

Coulson-type integral formulas for the general energy of a vertex

Lu Qiao, Shenggui Zhang, Jing Li, Nan Gao

School of Mathematics and Statistics

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

1 Scopus citations

Abstract

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently Arizmendi and Juárez-Romero proposed the concept of vertex energy and Arizmendi et al. further obtained a Coulson-type integral formula for the vertex energy of a graph. In this paper, we will introduce the concept of the general energy of a vertex, and give some Coulson-type integral formulas for the general energy of a vertex.

Original language	English
Article number	126565
Journal	Journal of Mathematical Analysis and Applications
Volume	517
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126565
State	Published - 1 Jan 2022

Keywords

Coulson-type integral formulas
General vertex energy
Graph energy

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10.1016/j.jmaa.2022.126565

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abstract = "The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently Arizmendi and Ju{\'a}rez-Romero proposed the concept of vertex energy and Arizmendi et al. further obtained a Coulson-type integral formula for the vertex energy of a graph. In this paper, we will introduce the concept of the general energy of a vertex, and give some Coulson-type integral formulas for the general energy of a vertex.",

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AU - Qiao, Lu

AU - Zhang, Shenggui

AU - Li, Jing

AU - Gao, Nan

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Y1 - 2022/1/1

N2 - The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently Arizmendi and Juárez-Romero proposed the concept of vertex energy and Arizmendi et al. further obtained a Coulson-type integral formula for the vertex energy of a graph. In this paper, we will introduce the concept of the general energy of a vertex, and give some Coulson-type integral formulas for the general energy of a vertex.

AB - The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently Arizmendi and Juárez-Romero proposed the concept of vertex energy and Arizmendi et al. further obtained a Coulson-type integral formula for the vertex energy of a graph. In this paper, we will introduce the concept of the general energy of a vertex, and give some Coulson-type integral formulas for the general energy of a vertex.

KW - Coulson-type integral formulas

KW - General vertex energy

KW - Graph energy

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

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ER -

Coulson-type integral formulas for the general energy of a vertex

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Keywords

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