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Harmonic Index and Harmonic Polynomial on Graph Operations

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Oct 2018 English Publisher:MDPI AGJournal:Symmetry, volume 10, page 456 (eissn: 2073-8994, Copyright policy )
Authors: Juan Carlos Hernández-Gómez; J. A. Méndez-Bermúdez; José M. Rodríguez 0001; José María Sigarreta;

doi: 10.3390/sym10100456

handle: 10016/28007

Harmonic Index and Harmonic Polynomial on Graph Operations

Abstract

Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O ( n 2 ) .

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Keywords

Algorithm, Harmonic polynomial, Products of graphs, Matemáticas, Harmonic index, harmonic index; harmonic polynomial; inverse degree index; products of graphs; algorithm, Inverse degree index

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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