On the Augmented Zagreb Index

zbMATH Open1463.05076arXiv1402.3078MaRDI QIDQ5118238

Author name not available (Why is that?)

Publication date: 7 September 2020

Abstract: Topological indices play an important role in mathematical chemistry especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). Recent research indicates that the augmented Zagreb index (AZI) possess the best correlating ability among several topological indices. The main purpose of the current study is to establish some mathematical properties of this index, or more precisely, to report tight bounds for the AZI of chemical bicyclic and chemical unicyclic graphs. A Nordhaus-Gaddum-type result for the AZI (of connected graph whose complement is connected) is also derived.

Full work available at URL: https://arxiv.org/abs/1402.3078

zbMATH Keywords

topological index augmented Zagreb index chemical bicyclic graph Nordhaus-Gaddum type relations chemical unicyclic graph

Mathematics Subject Classification ID

Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Vertex degrees (05C07) Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) (05C09) Chemical graph theory (05C92)

Related Items (8)

Maximal augmented Zagreb index of trees with given diameter ⋮ A note on the first reformulated Zagreb index ⋮ Some bounds of weighted entropies with augmented Zagreb index edge weights ⋮ Further inequalities between vertex-degree-based topological indices ⋮ On the maximal augmented Zagreb index of unicyclic graphs with given girth ⋮ The degree-based topological indices for two special families of graphs of diameter three ⋮ Title not available (Why is that?) ⋮ Unicyclic and bicyclic graphs with minimal augmented Zagreb index

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