Seidel-Estrada index

Jalal Askari; Ali Iranmanesh; Kinkar Ch Das

doi:10.1186/s13660-016-1061-9

Seidel-Estrada index

Jalal Askari, Ali Iranmanesh, Kinkar Ch Das

Department of Mathematics

Tarbiat Modarres University

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

8 Scopus citations

Abstract

Let G be a simple graph with n vertices and (Formula presented.) -adjacency matrix A. As usual, (Formula presented.) denotes the Seidel matrix of the graph G. Suppose (Formula presented.) and (Formula presented.) are the eigenvalues of the adjacency matrix and the Seidel matrix of G, respectively. The Estrada index of the graph G is defined as (Formula presented.). We define and investigate the Seidel-Estrada index, (Formula presented.). In this paper the basic properties of the Seidel-Estrada index are investigated. Moreover, some lower and upper bounds for the Seidel-Estrada index in terms of the number of vertices are obtained. In addition, some relations between (Formula presented.) and the Seidel energy (Formula presented.) are presented.

Original language	English
Article number	120
Journal	Journal of Inequalities and Applications
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1186/s13660-016-1061-9
State	Published - 1 Dec 2016

Keywords

eigenvalue
Seidel matrix
Seidel-Estrada index

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10.1186/s13660-016-1061-9

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title = "Seidel-Estrada index",

abstract = "Let G be a simple graph with n vertices and (Formula presented.) -adjacency matrix A. As usual, (Formula presented.) denotes the Seidel matrix of the graph G. Suppose (Formula presented.) and (Formula presented.) are the eigenvalues of the adjacency matrix and the Seidel matrix of G, respectively. The Estrada index of the graph G is defined as (Formula presented.). We define and investigate the Seidel-Estrada index, (Formula presented.). In this paper the basic properties of the Seidel-Estrada index are investigated. Moreover, some lower and upper bounds for the Seidel-Estrada index in terms of the number of vertices are obtained. In addition, some relations between (Formula presented.) and the Seidel energy (Formula presented.) are presented.",

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author = "Jalal Askari and Ali Iranmanesh and Das, \{Kinkar Ch\}",

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TY - JOUR

T1 - Seidel-Estrada index

AU - Askari, Jalal

AU - Iranmanesh, Ali

AU - Das, Kinkar Ch

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let G be a simple graph with n vertices and (Formula presented.) -adjacency matrix A. As usual, (Formula presented.) denotes the Seidel matrix of the graph G. Suppose (Formula presented.) and (Formula presented.) are the eigenvalues of the adjacency matrix and the Seidel matrix of G, respectively. The Estrada index of the graph G is defined as (Formula presented.). We define and investigate the Seidel-Estrada index, (Formula presented.). In this paper the basic properties of the Seidel-Estrada index are investigated. Moreover, some lower and upper bounds for the Seidel-Estrada index in terms of the number of vertices are obtained. In addition, some relations between (Formula presented.) and the Seidel energy (Formula presented.) are presented.

AB - Let G be a simple graph with n vertices and (Formula presented.) -adjacency matrix A. As usual, (Formula presented.) denotes the Seidel matrix of the graph G. Suppose (Formula presented.) and (Formula presented.) are the eigenvalues of the adjacency matrix and the Seidel matrix of G, respectively. The Estrada index of the graph G is defined as (Formula presented.). We define and investigate the Seidel-Estrada index, (Formula presented.). In this paper the basic properties of the Seidel-Estrada index are investigated. Moreover, some lower and upper bounds for the Seidel-Estrada index in terms of the number of vertices are obtained. In addition, some relations between (Formula presented.) and the Seidel energy (Formula presented.) are presented.

KW - eigenvalue

KW - Seidel matrix

KW - Seidel-Estrada index

UR - https://www.scopus.com/pages/publications/84963780250

U2 - 10.1186/s13660-016-1061-9

DO - 10.1186/s13660-016-1061-9

M3 - Article

AN - SCOPUS:84963780250

SN - 1025-5834

VL - 2016

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 120

ER -

Seidel-Estrada index

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