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New lower bounds for the second variable Zagreb index

Author

Listed:
  • Álvaro Martínez-Pérez

    (Facultad CC. Sociales de Talavera)

  • José M. Rodríguez

    (Universidad Carlos III de Madrid)

Abstract

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index $$M_2^{\alpha }$$ M 2 α , and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randić, the second Zagreb and the modified Zagreb indices.

Suggested Citation

  • Álvaro Martínez-Pérez & José M. Rodríguez, 2018. "New lower bounds for the second variable Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 194-210, July.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0293-7
    DOI: 10.1007/s10878-018-0293-7
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    References listed on IDEAS

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    1. N/A, 2004. "Index for 2004," European Union Politics, , vol. 5(4), pages 511-512, December.
    2. Milovanović, E.I. & Milovanović, I.Ž. & Dolićanin, E.Ć. & Glogić, E., 2016. "A note on the first reformulated Zagreb index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 16-20.
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