Comparison of wiener index and zagreb eccentricity indices

Kexiang Xu; Kinkar Chandra Das; Sandi Klavžar; Huimin Li

Comparison of wiener index and zagreb eccentricity indices

Kexiang Xu
, Kinkar Chandra Das
, Sandi Klavžar
, Huimin Li

Department of Mathematics

Nanjing University of Aeronautics and Astronautics
University of Ljubljana
University of Maribor
Institute of Mathematics, Physics and Mechanics

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

15 Scopus citations

Abstract

The first and the second Zagreb eccentricity index of a graph G are defined as E₁(G) = ^P_v∈V (G₎ εG(v)² and E₂(G) = ^P_uv∈E(G₎ εG(u)εG(v), respectively, where εG(v) is the eccentricity of a vertex v. In this paper the invariants E₁, E₂, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E₂(T) holds, and if the diameter of T is large, then W(T) < E₁(T) holds.

Original language	English
Pages (from-to)	595-610
Number of pages	16
Journal	Match
Volume	84
Issue number	3
State	Published - 2020

Cite this

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title = "Comparison of wiener index and zagreb eccentricity indices",

abstract = "The first and the second Zagreb eccentricity index of a graph G are defined as E1(G) = Pv∈V (G) εG(v)2 and E2(G) = Puv∈E(G) εG(u)εG(v), respectively, where εG(v) is the eccentricity of a vertex v. In this paper the invariants E1, E2, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E2(T) holds, and if the diameter of T is large, then W(T) < E1(T) holds.",

author = "Kexiang Xu and Das, \{Kinkar Chandra\} and Sandi Klav{\v z}ar and Huimin Li",

year = "2020",

language = "English",

volume = "84",

pages = "595--610",

journal = "Match",

issn = "0340-6253",

publisher = "University of Kragujevac, Faculty of Science",

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T1 - Comparison of wiener index and zagreb eccentricity indices

AU - Xu, Kexiang

AU - Das, Kinkar Chandra

AU - Klavžar, Sandi

AU - Li, Huimin

PY - 2020

Y1 - 2020

N2 - The first and the second Zagreb eccentricity index of a graph G are defined as E1(G) = Pv∈V (G) εG(v)2 and E2(G) = Puv∈E(G) εG(u)εG(v), respectively, where εG(v) is the eccentricity of a vertex v. In this paper the invariants E1, E2, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E2(T) holds, and if the diameter of T is large, then W(T) < E1(T) holds.

AB - The first and the second Zagreb eccentricity index of a graph G are defined as E1(G) = Pv∈V (G) εG(v)2 and E2(G) = Puv∈E(G) εG(u)εG(v), respectively, where εG(v) is the eccentricity of a vertex v. In this paper the invariants E1, E2, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E2(T) holds, and if the diameter of T is large, then W(T) < E1(T) holds.

UR - https://www.scopus.com/pages/publications/85091787890

M3 - Article

AN - SCOPUS:85091787890

SN - 0340-6253

VL - 84

SP - 595

EP - 610

JO - Match

JF - Match

IS - 3

ER -

Comparison of wiener index and zagreb eccentricity indices

Abstract

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