Comparing the excepted values of atom-bond connectivity and geometric-arithmetic indices in random spiro chains

Area of Science:

• Chemical graph theory
• Computational chemistry
• Structure-property relationships

Background:

• The atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are established topological indices.
• These indices are valuable in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies.
• Spiro chains represent a class of unbranched polycyclic aromatic hydrocarbons.

Purpose of the Study:

• To derive explicit formulas for the expected values of the ABC and GA indices in random spiro chains.
• To calculate the average values of these indices for spiro chains with n hexagons.
• To compare the expected and average values of the ABC and GA indices within this class of chemical structures.

Main Methods:

• Utilizing graph theory principles to analyze spiro chain structures.
• Deriving mathematical formulas for topological indices based on graph properties.
• Statistical analysis to compute expected and average values.

Main Results:

• Explicit formulas for the expected values of ABC and GA indices in random spiro chains were obtained.
• The average values of ABC and GA indices for spiro chains with n hexagons were presented.
• A comparative analysis of the expected and average values of these indices was performed.

Conclusions:

• The derived formulas provide a basis for understanding the behavior of ABC and GA indices in spiro chains.
• This research contributes to the application of topological indices in predicting properties of polycyclic aromatic hydrocarbons.
• The findings facilitate further investigations into the relationship between molecular structure and chemical properties.