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New upper bounds for the forgotten index among bicyclic graphs
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  • Jonnathan Rodriguez,
  • Akbar Jahanbani,
  • Seyed Mahmoud Sheikholeslami,
  • Reza Rasi,
  • L Shahbazi
Jonnathan Rodriguez
Universidad de Antofagasta
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Akbar Jahanbani
Shahrood University of Technology
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Seyed Mahmoud Sheikholeslami
Azarbaijan Shahid Madani University
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Reza Rasi
Azarbaijan Shahid Madani University
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L Shahbazi
Azarbaijan Shahid Madani University
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Abstract

The forgotten topological index of a graph $G$, denoted by $F(G)$, is defined as the sum of weights $d(u)^{2}+d(v)^{2}$ over all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$. In this paper, we give sharp upper bounds of the F-index (forgotten topological index) over bicyclic graphs, in terms of the order and maximum degree.