On two eccentricity-based topological indices of graphs

Kexiang Xu; Yaser Alizadeh; Kinkar Ch Das

doi:10.1016/j.dam.2017.08.010

On two eccentricity-based topological indices of graphs

Kexiang Xu, Yaser Alizadeh, Kinkar Ch Das

Department of Mathematics

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

27 Scopus citations

Abstract

For a connected graph G, the eccentric connectivity index (ECI) and connective eccentricity index (CEI) of G are, respectively, defined as ξ^c(G)=∑_{v_i∈V(G)}deg_G(v_i)ε_G(v_i), ξ^ce(G)=∑_{v_i∈V(G)}[formula presented] where deg_G(v_i) is the degree of v_i in G and ε_G(v_i) denotes the eccentricity of vertex v_i in G. In this paper we study on the difference of ECI and CEI of graphs G, denoted by ξ^D(G)=ξ^c(G)−ξ^ce(G). We determine the upper and lower bounds on ξ^D(T) and the corresponding extremal trees among all trees of order n. Moreover, the extremal trees with respect to ξ^D are completely characterized among all trees with given diameter d. And we also characterize some extremal general graphs with respect to ξ^D. Finally we propose that some comparative relations between CEI and ECI are proposed on general graphs with given number of pendant vertices.

Original language	English
Pages (from-to)	240-251
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	233
DOIs	https://doi.org/10.1016/j.dam.2017.08.010
State	Published - 31 Dec 2017

Keywords

Connective eccentricity index
Diameter
Eccentric connectivity index
Eccentricity

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10.1016/j.dam.2017.08.010

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@article{3582639d6e2e4045945a6e4975d75c8e,

title = "On two eccentricity-based topological indices of graphs",

abstract = "For a connected graph G, the eccentric connectivity index (ECI) and connective eccentricity index (CEI) of G are, respectively, defined as ξc(G)=∑vi∈V(G)degG(vi)εG(vi), ξce(G)=∑vi∈V(G)[formula presented] where degG(vi) is the degree of vi in G and εG(vi) denotes the eccentricity of vertex vi in G. In this paper we study on the difference of ECI and CEI of graphs G, denoted by ξD(G)=ξc(G)−ξce(G). We determine the upper and lower bounds on ξD(T) and the corresponding extremal trees among all trees of order n. Moreover, the extremal trees with respect to ξD are completely characterized among all trees with given diameter d. And we also characterize some extremal general graphs with respect to ξD. Finally we propose that some comparative relations between CEI and ECI are proposed on general graphs with given number of pendant vertices.",

keywords = "Connective eccentricity index, Diameter, Eccentric connectivity index, Eccentricity",

author = "Kexiang Xu and Yaser Alizadeh and Das, \{Kinkar Ch\}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = dec,

day = "31",

doi = "10.1016/j.dam.2017.08.010",

language = "English",

volume = "233",

pages = "240--251",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - On two eccentricity-based topological indices of graphs

AU - Xu, Kexiang

AU - Alizadeh, Yaser

AU - Das, Kinkar Ch

PY - 2017/12/31

Y1 - 2017/12/31

N2 - For a connected graph G, the eccentric connectivity index (ECI) and connective eccentricity index (CEI) of G are, respectively, defined as ξc(G)=∑vi∈V(G)degG(vi)εG(vi), ξce(G)=∑vi∈V(G)[formula presented] where degG(vi) is the degree of vi in G and εG(vi) denotes the eccentricity of vertex vi in G. In this paper we study on the difference of ECI and CEI of graphs G, denoted by ξD(G)=ξc(G)−ξce(G). We determine the upper and lower bounds on ξD(T) and the corresponding extremal trees among all trees of order n. Moreover, the extremal trees with respect to ξD are completely characterized among all trees with given diameter d. And we also characterize some extremal general graphs with respect to ξD. Finally we propose that some comparative relations between CEI and ECI are proposed on general graphs with given number of pendant vertices.

AB - For a connected graph G, the eccentric connectivity index (ECI) and connective eccentricity index (CEI) of G are, respectively, defined as ξc(G)=∑vi∈V(G)degG(vi)εG(vi), ξce(G)=∑vi∈V(G)[formula presented] where degG(vi) is the degree of vi in G and εG(vi) denotes the eccentricity of vertex vi in G. In this paper we study on the difference of ECI and CEI of graphs G, denoted by ξD(G)=ξc(G)−ξce(G). We determine the upper and lower bounds on ξD(T) and the corresponding extremal trees among all trees of order n. Moreover, the extremal trees with respect to ξD are completely characterized among all trees with given diameter d. And we also characterize some extremal general graphs with respect to ξD. Finally we propose that some comparative relations between CEI and ECI are proposed on general graphs with given number of pendant vertices.

KW - Connective eccentricity index

KW - Diameter

KW - Eccentric connectivity index

KW - Eccentricity

UR - https://www.scopus.com/pages/publications/85029657889

U2 - 10.1016/j.dam.2017.08.010

DO - 10.1016/j.dam.2017.08.010

M3 - Article

AN - SCOPUS:85029657889

SN - 0166-218X

VL - 233

SP - 240

EP - 251

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

On two eccentricity-based topological indices of graphs

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