Alkanes with the First Three Maximal/Minimal Modified First Zagreb Connection Indices.

The modified first Zagreb connection index ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi> <mml:msubsup><mml:mi>C</mml:mi> <mml:mn>1</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> </mml:math> ) is a molecular descriptor, which was initially appeared within a formula of the total electron energy of alternant hydrocarbons in 1972. In a recent paper [A. Ali, N. Trinajstić, A novel/old modification of the first Zagreb index, Mol. Inform. 37 (2018) 1800008], it was observed that the molecular descriptor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi> <mml:msubsup><mml:mi>C</mml:mi> <mml:mn>1</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> </mml:math> correlates well with the entropy and acentric factor of octane isomers. In this article, the molecules with the first three maximal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi> <mml:msubsup><mml:mi>C</mml:mi> <mml:mn>1</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> </mml:math> values as well as the first three minimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi> <mml:msubsup><mml:mi>C</mml:mi> <mml:mn>1</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> </mml:math> values are determined from the family of all alkanes with n carbon atoms, for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>6</mml:mn></mml:mrow> </mml:math> . This extends the main results of the aforementioned paper.