f -Polynomial on Some Graph Operations

Walter Carballosa, José Manuel Rodríguez, José María Sigarreta and Nodari Vakhania
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Walter Carballosa: Department of Mathematics and Statistics, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA
José Manuel Rodríguez: Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
José María Sigarreta: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54 Col. Garita, 39650 Acapulco, Mexico
Nodari Vakhania: Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001 Col. Chamilpa, 62209 Cuernavaca, Mexico

Mathematics, 2019, vol. 7, issue 11, 1-18

Abstract: 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.

Keywords: inverse degree index; generalized first Zagreb index; sum lordeg index; corona product; join of graphs; line graph; Mycielskian graph; polynomials in graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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