New upper bounds for the forgotten index among bicyclic graphs

TL;DR

This paper establishes sharp upper bounds for the forgotten topological index in bicyclic graphs, relating it to the graph's order and maximum degree, advancing understanding of graph invariants.

Contribution

It provides the first sharp upper bounds for the forgotten index specifically in bicyclic graphs, based on order and maximum degree.

Findings

Derived sharp upper bounds for F-index in bicyclic graphs.

Bound expressed in terms of graph order and maximum degree.

Enhances understanding of topological indices in complex graphs.

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.