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\begin{document}

\title{The comparative analysis of the multiplicative atom-bond connectivity
and geometric-arithmetic indices in random polyphenyl and spiro chains}



\author[1]{Zahid Raza}%
\affil[1]{University of Sharjah}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
The polyphenyl chains with \$n\$ hexagons are the special graphs of
unbranched polycyclic aromatic hydrocarbons. The objective of this study
is to find the expected values of the multiplicative version of the
atomic-bond connectivity index and geometric-arithmetic index of this
class of special hydrocarbons. The average values of these two indices
with respect to the set of all polyphenyl chains have been determined.
Finally, the comparisons between the expected values of the
aforementioned indices in the random polyphenyl and spiro chains, have
been outlined.%
\end{abstract}%



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