On Average Eccentricity of Graphs

Kinkar Ch Das; A. Dilek Maden; I. Naci Cangül; A. Sinan Çevik

doi:10.1007/s40010-016-0315-8

On Average Eccentricity of Graphs

Kinkar Ch Das, A. Dilek Maden, I. Naci Cangül, A. Sinan Çevik

Department of Mathematics

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

15 Scopus citations

Abstract

The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and GA₁ index.

Original language	English
Pages (from-to)	23-30
Number of pages	8
Journal	Proceedings of the National Academy of Sciences India Section A - Physical Sciences
Volume	87
Issue number	1
DOIs	https://doi.org/10.1007/s40010-016-0315-8
State	Published - 1 Mar 2017

Keywords

Atom-bond connectivity index (ABC)
Average eccentricity
Clique number
Distances
Eccentricity
Energy
First Zagreb index
Geometric–arithmetic index (GA)
Graph
Independence number

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10.1007/s40010-016-0315-8

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title = "On Average Eccentricity of Graphs",

abstract = "The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and GA1 index.",

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doi = "10.1007/s40010-016-0315-8",

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T1 - On Average Eccentricity of Graphs

AU - Das, Kinkar Ch

AU - Maden, A. Dilek

AU - Cangül, I. Naci

AU - Çevik, A. Sinan

PY - 2017/3/1

Y1 - 2017/3/1

N2 - The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and GA1 index.

AB - The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and GA1 index.

KW - Atom-bond connectivity index (ABC)

KW - Average eccentricity

KW - Clique number

KW - Distances

KW - Eccentricity

KW - Energy

KW - First Zagreb index

KW - Geometric–arithmetic index (GA)

KW - Graph

KW - Independence number

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U2 - 10.1007/s40010-016-0315-8

DO - 10.1007/s40010-016-0315-8

M3 - Article

AN - SCOPUS:85013174058

SN - 0369-8203

VL - 87

SP - 23

EP - 30

JO - Proceedings of the National Academy of Sciences India Section A - Physical Sciences

JF - Proceedings of the National Academy of Sciences India Section A - Physical Sciences

IS - 1

ER -

On Average Eccentricity of Graphs

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Keywords

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