On the n-vertex trees with sixth to fifteenth maximum harmonic indices

Akbar Ali; Selvaraj Balachandran; Suresh Elumalai; Toufik Mansour

doi:10.1007/s13370-019-00758-0

On the n-vertex trees with sixth to fifteenth maximum harmonic indices

Akbar Ali, Selvaraj Balachandran, Suresh Elumalai, Toufik Mansour

Department of Mathematics

University of Haifa

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

Abstract

The harmonic index of a graph G is denoted by H(G) and is defined as H(G)=∑uv∈E(G)2du+dv, where d_u, d_v denote the degrees of the vertices u, v, respectively, of G and E(G) is the edge set of G. In this paper, the graphs having sixth to fifteenth maximum harmonic indices are characterized from the class of all n-vertex trees for sufficiently large n.

Original language	American English
Pages (from-to)	771-780
Number of pages	10
Journal	Afrika Matematika
Volume	31
Issue number	5-6
DOIs	https://doi.org/10.1007/s13370-019-00758-0
State	Published - 1 Sep 2020

Keywords

Extremal problem
Harmonic index
Trees

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s13370-019-00758-0

Cite this

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abstract = "The harmonic index of a graph G is denoted by H(G) and is defined as H(G)=∑uv∈E(G)2du+dv, where du, dv denote the degrees of the vertices u, v, respectively, of G and E(G) is the edge set of G. In this paper, the graphs having sixth to fifteenth maximum harmonic indices are characterized from the class of all n-vertex trees for sufficiently large n.",

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author = "Akbar Ali and Selvaraj Balachandran and Suresh Elumalai and Toufik Mansour",

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PY - 2020/9/1

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N2 - The harmonic index of a graph G is denoted by H(G) and is defined as H(G)=∑uv∈E(G)2du+dv, where du, dv denote the degrees of the vertices u, v, respectively, of G and E(G) is the edge set of G. In this paper, the graphs having sixth to fifteenth maximum harmonic indices are characterized from the class of all n-vertex trees for sufficiently large n.

AB - The harmonic index of a graph G is denoted by H(G) and is defined as H(G)=∑uv∈E(G)2du+dv, where du, dv denote the degrees of the vertices u, v, respectively, of G and E(G) is the edge set of G. In this paper, the graphs having sixth to fifteenth maximum harmonic indices are characterized from the class of all n-vertex trees for sufficiently large n.

KW - Extremal problem

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KW - Trees

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ER -

On the n-vertex trees with sixth to fifteenth maximum harmonic indices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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