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f -Polynomial on Some Graph Operations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Walter Carballosa & José Manuel Rodríguez & José María Sigarreta & Nodari Vakhania, 2019. "f -Polynomial on Some Graph Operations," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1074-:d:284867
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    References listed on IDEAS

    as
    1. Su, Guifu & Xu, Lan, 2015. "Topological indices of the line graph of subdivision graphs and their Schur-bounds," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 395-401.
    2. Borovićanin, Bojana & Furtula, Boris, 2016. "On extremal Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 208-218.
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