Some properties of the Zagreb eccentricity indices

Kinkar Ch Das; Dae Won Lee; Ante Graovac

doi:10.26493/1855-3974.237.48a

Some properties of the Zagreb eccentricity indices

Kinkar Ch Das, Dae Won Lee, Ante Graovac

Department of Mathematics

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

48 Scopus citations

Abstract

The concept of Zagreb eccentricity (E₁ and E₂) indices was introduced in the chemical graph theory very recently [5, 12]. The first Zagreb eccentricity (E₁) and the second Zagreb eccentricity (E₂) indices of a graph G are defined as {equation presented} and {equation presented}, where E(G) is the edge set and e_i is the eccentricity of the vertex υ_i in G. In this paper we give some lower and upper bounds on the first Zagreb eccentricity and the second Zagreb eccentricity indices of trees and graphs, and also characterize the extremal graphs.

Original language	English
Pages (from-to)	117-125
Number of pages	9
Journal	Ars Mathematica Contemporanea
Volume	6
Issue number	1
DOIs	https://doi.org/10.26493/1855-3974.237.48a
State	Published - 2013

Keywords

Diameter
Eccentricity
First Zagreb eccentricity index
Graph
Second Zagreb eccentricity index

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10.26493/1855-3974.237.48a

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abstract = "The concept of Zagreb eccentricity (E1 and E2) indices was introduced in the chemical graph theory very recently [5, 12]. The first Zagreb eccentricity (E1) and the second Zagreb eccentricity (E2) indices of a graph G are defined as \{equation presented\} and \{equation presented\}, where E(G) is the edge set and ei is the eccentricity of the vertex υi in G. In this paper we give some lower and upper bounds on the first Zagreb eccentricity and the second Zagreb eccentricity indices of trees and graphs, and also characterize the extremal graphs.",

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AU - Das, Kinkar Ch

AU - Lee, Dae Won

AU - Graovac, Ante

PY - 2013

Y1 - 2013

N2 - The concept of Zagreb eccentricity (E1 and E2) indices was introduced in the chemical graph theory very recently [5, 12]. The first Zagreb eccentricity (E1) and the second Zagreb eccentricity (E2) indices of a graph G are defined as {equation presented} and {equation presented}, where E(G) is the edge set and ei is the eccentricity of the vertex υi in G. In this paper we give some lower and upper bounds on the first Zagreb eccentricity and the second Zagreb eccentricity indices of trees and graphs, and also characterize the extremal graphs.

AB - The concept of Zagreb eccentricity (E1 and E2) indices was introduced in the chemical graph theory very recently [5, 12]. The first Zagreb eccentricity (E1) and the second Zagreb eccentricity (E2) indices of a graph G are defined as {equation presented} and {equation presented}, where E(G) is the edge set and ei is the eccentricity of the vertex υi in G. In this paper we give some lower and upper bounds on the first Zagreb eccentricity and the second Zagreb eccentricity indices of trees and graphs, and also characterize the extremal graphs.

KW - Diameter

KW - Eccentricity

KW - First Zagreb eccentricity index

KW - Graph

KW - Second Zagreb eccentricity index

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VL - 6

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EP - 125

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

IS - 1

ER -

Some properties of the Zagreb eccentricity indices

Abstract

Keywords

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