Bounds on the General Eccentric Connectivity Index

Xinhong Yu; Muhammad Imran; Aisha Javed; Muhammad Kamran Jamil; Xuewu Zuo

doi:10.3390/sym14122560

Bounds on the General Eccentric Connectivity Index

Xinhong Yu, Muhammad Imran, Aisha Javed, Muhammad Kamran Jamil, Xuewu Zuo

Department of Mathematical Sciences

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

2 Citations (Scopus)

Abstract

The general eccentric connectivity index of a graph R is defined as (Formula presented.), where (Formula presented.) is any real number, (Formula presented.) and (Formula presented.) represent the eccentricity and the degree of the vertex u in R, respectively. In this paper, some bounds on the general eccentric connectivity index are proposed in terms of graph-theoretic parameters, namely, order, radius, independence number, eccentricity, pendent vertices and cut edges. Moreover, extremal graphs are characterized by these bounds.

Original language	English
Article number	2560
Journal	Symmetry
Volume	14
Issue number	12
DOIs	https://doi.org/10.3390/sym14122560
Publication status	Published - Dec 2022

Keywords

eccentric connectivity index
eccentricity of vertex
extremal graphs
general eccentric connectivity index

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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10.3390/sym14122560

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title = "Bounds on the General Eccentric Connectivity Index",

abstract = "The general eccentric connectivity index of a graph R is defined as (Formula presented.), where (Formula presented.) is any real number, (Formula presented.) and (Formula presented.) represent the eccentricity and the degree of the vertex u in R, respectively. In this paper, some bounds on the general eccentric connectivity index are proposed in terms of graph-theoretic parameters, namely, order, radius, independence number, eccentricity, pendent vertices and cut edges. Moreover, extremal graphs are characterized by these bounds.",

keywords = "eccentric connectivity index, eccentricity of vertex, extremal graphs, general eccentric connectivity index",

author = "Xinhong Yu and Muhammad Imran and Aisha Javed and Jamil, {Muhammad Kamran} and Xuewu Zuo",

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T1 - Bounds on the General Eccentric Connectivity Index

AU - Yu, Xinhong

AU - Imran, Muhammad

AU - Javed, Aisha

AU - Jamil, Muhammad Kamran

AU - Zuo, Xuewu

PY - 2022/12

Y1 - 2022/12

N2 - The general eccentric connectivity index of a graph R is defined as (Formula presented.), where (Formula presented.) is any real number, (Formula presented.) and (Formula presented.) represent the eccentricity and the degree of the vertex u in R, respectively. In this paper, some bounds on the general eccentric connectivity index are proposed in terms of graph-theoretic parameters, namely, order, radius, independence number, eccentricity, pendent vertices and cut edges. Moreover, extremal graphs are characterized by these bounds.

AB - The general eccentric connectivity index of a graph R is defined as (Formula presented.), where (Formula presented.) is any real number, (Formula presented.) and (Formula presented.) represent the eccentricity and the degree of the vertex u in R, respectively. In this paper, some bounds on the general eccentric connectivity index are proposed in terms of graph-theoretic parameters, namely, order, radius, independence number, eccentricity, pendent vertices and cut edges. Moreover, extremal graphs are characterized by these bounds.

KW - eccentric connectivity index

KW - eccentricity of vertex

KW - extremal graphs

KW - general eccentric connectivity index

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VL - 14

JO - Symmetry

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IS - 12

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ER -

Bounds on the General Eccentric Connectivity Index

Abstract

Keywords

ASJC Scopus subject areas

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