Bounds on the Arithmetic-Geometric Index

The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with re...

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Published in:Symmetry (Basel) 2021-04, Vol.13 (4), p.689
Main Authors: Rodríguez, José M., Sánchez, José L., Sigarreta, José M., Tourís, Eva
Format: Article
Language:English
Subjects:
Arithmetic
arithmetic-geometric index
general atom-bond connectivity index
Graph theory
Graphs
Inequality
Mathematical analysis
symmetric division deg index
variable Zagreb index
vertex-degree-based topological index
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description The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with respect to them. Several bounds are based on other indices, such as the second variable Zagreb index or the general atom-bond connectivity index), and some of them involve some parameters, such as the number of edges, the maximum degree, or the minimum degree of the graph. In most bounds, the graphs for which equality is attained are regular or biregular, or star graphs.
doi_str_mv 10.3390/sym13040689
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subjects Arithmetic
arithmetic-geometric index
general atom-bond connectivity index
Graph theory
Graphs
Inequality
Mathematical analysis
symmetric division deg index
variable Zagreb index
vertex-degree-based topological index
title Bounds on the Arithmetic-Geometric Index
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