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Open AccessFeature PaperArticle

Harmonic Index and Harmonic Polynomial on Graph Operations

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Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, Acalpulco Gro. 39650, Mexico
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Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
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Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, Spain
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Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 456; https://doi.org/10.3390/sym10100456
Received: 3 August 2018 / Revised: 27 September 2018 / Accepted: 28 September 2018 / Published: 1 October 2018
(This article belongs to the Special Issue Symmetry in Graph Theory)
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 ) . View Full-Text
Keywords: harmonic index; harmonic polynomial; inverse degree index; products of graphs; algorithm harmonic index; harmonic polynomial; inverse degree index; products of graphs; algorithm
MDPI and ACS Style

Hernández-Gómez, J.C.; Méndez-Bermúdez, J.A.; Rodríguez, J.M.; Sigarreta, J.M. Harmonic Index and Harmonic Polynomial on Graph Operations. Symmetry 2018, 10, 456.

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