On extremal trees with respect to the F-index

Authors

  • Hosam Abdo Freie Universität Berlin Institute of Computer Science Takustraße 9 D-14195 Berlin Germany
  • Darko Dimitrov Hochschule für Technik und Wirtschaft Berlin Wilhelminenhofstraße 75A D--12459 Berlin Germany
  • Ivan Gutman University of Kragujevac Faculty of Science Serbia & State University of Novi Pazar, Novi Pazar, Serbia

Keywords:

Topological indices, general first Zagreb index, F-index, trees, molecular trees

Abstract

In a study on the structure--dependency of the total $\pi$-electron energy from 1972,Trinajsti\'c and one of the present authors have shown that it depends on the sums$\sum_{v\in V}d(v)^2$ and $\sum_{v\in V}d(v)^3$, where $d(v)$ is the degree of a vertex $v$ of the underlying molecular graph $G$. The first sum was later named {\it first Zagreb index}and over the years became one of the most investigated graph--based molecularstructure descriptors. On the other hand, the second sum, except in very fewworks on the general first Zagreb index and the zeroth--order general Randi\'c index, has been almost completely neglected. Recently, this second sum was named{\it forgotten index}, or shortly the $F$-index, and shown to have anexceptional applicative potential. In this paper we examine the trees extremal with respect to the $F$-index

References

Carlos Da Fonseca

Assistant Professor

Kuwait University

Faculty of Science

Department of Mathematics

Milica Andelic

Assistant Professor

Kuwait University

Faculty of Science

Department of Mathematics

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Published

21-07-2017