A Novel/Old Modification of the First Zagreb Index.

Area of Science:

• Chemical Graph Theory
• Computational Chemistry
• Structure-Property Relationships

Background:

• The first Zagreb index relates molecular graph degrees to electron energy (Eπ).
• A related descriptor, the modified first Zagreb connection index (ZC1*), was identified but not explicitly studied.
• ZC1* is proposed to also influence Eπ in alternant hydrocarbons.

Purpose of the Study:

• To investigate the chemical applicability of the ZC1* descriptor.
• To establish basic properties of the ZC1* descriptor.
• To determine alkanes with maximum and minimum ZC1* values for a fixed number of carbon atoms.

Main Methods:

• Analysis of ZC1* for octane isomers.
• Establishment of fundamental properties of ZC1*.
• Identification of alkanes with extremal ZC1* values.

Main Results:

• The chemical applicability of ZC1* for octane isomers was evaluated.
• Key properties of ZC1* were elucidated.
• Alkanes exhibiting maximum and minimum ZC1* values were identified.

Conclusions:

• The ZC1* descriptor shows relevance in chemical applications, particularly for octane isomers.
• The study provides foundational insights into the ZC1* descriptor.
• Extremal ZC1* values for alkanes with a fixed carbon count were determined.