Further Results for Some Eccentric Based Indices

Area of Science:

• Chemical graph theory
• Mathematical chemistry

Background:

• Topological indices are crucial for understanding molecular topology in theoretical chemistry.
• Eccentricity-based topological indices provide valuable insights into molecular structure.

Purpose of the Study:

• To derive novel lower and upper bounds for specific eccentric-based topological indices.
• To advance the application of mathematical methods in analyzing chemical structures.

Main Methods:

• The study employed the comparison theorem for integrals.
• This integral comparison method was utilized to establish new bounds.

Main Results:

• New bounds were successfully determined for the eccentric-based harmonic index and the atom-bond connectivity index.
• The derived bounds demonstrate improvement over previously reported results in the literature.

Conclusions:

• This research introduces a new mathematical technique for calculating bounds of eccentric-based topological indices.
• The findings contribute to the field of chemical graph theory by providing enhanced analytical tools for molecular topology.