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f-Polynomial on Some Graph Operations

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Department of Mathematics and Statistics, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA
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Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
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Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54 Col. Garita, 39650 Acapulco, Mexico
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Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001 Col. Chamilpa, 62209 Cuernavaca, Mexico
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1074; https://doi.org/10.3390/math7111074
Received: 20 September 2019 / Revised: 2 November 2019 / Accepted: 3 November 2019 / Published: 8 November 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
Given any function f : Z + R + , let us define the f-index I f ( G ) = u V ( G ) f ( d u ) and the f-polynomial P f ( G , x ) = u V ( G ) x 1 / f ( d u ) 1 , for x > 0 . In addition, we define P f ( G , 0 ) = lim x 0 + P f ( G , x ) . We use the f-polynomial of a large family of topological indices in order to study mathematical relations of the inverse degree, the generalized first Zagreb, and the sum lordeg indices, among others. In this paper, using this f-polynomial, we obtain several properties of these indices of some classical graph operations that include corona product and join, line, and Mycielskian, among others. View Full-Text
Keywords: inverse degree index; generalized first Zagreb index; sum lordeg index; corona product; join of graphs; line graph; Mycielskian graph; polynomials in graphs inverse degree index; generalized first Zagreb index; sum lordeg index; corona product; join of graphs; line graph; Mycielskian graph; polynomials in graphs
MDPI and ACS Style

Carballosa, W.; Rodríguez, J.M.; Sigarreta, J.M.; Vakhania, N. f-Polynomial on Some Graph Operations. Mathematics 2019, 7, 1074.

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