The Alkanes with Maximum Wiener Polarity Index.

The Wiener polarity index (usually denoted by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>W</mml:mi> <mml:mi>p</mml:mi></mml:msub> </mml:math> ) of an alkane is the number of unordered pairs of carbon atoms which are separated by three carbon-carbon bonds. This topological index <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>W</mml:mi> <mml:mi>p</mml:mi></mml:msub> </mml:math> is useful for predicting the boiling points of alkanes. Deng [MATCH Commun. Math. Comput. Chem. 66 (2011) 305] proved that the maximum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>W</mml:mi> <mml:mi>p</mml:mi></mml:msub> </mml:math> value among all alkanes, with n carbon atoms, is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>3</mml:mn> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mn>15</mml:mn></mml:mrow> </mml:math> . The main purpose of present paper is to find all those alkanes with n carbon atoms, which attain the maximum value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>W</mml:mi> <mml:mi>p</mml:mi></mml:msub> </mml:math> .