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\begin{document}

\title{Calculation and analysis of the strong prism of the
octagonal-quadrilateral networks}



\author[1]{Jia-bao Liu}%
\author[2]{Kang Wang}%
\author[1]{Ya-Qian Zheng}%
\affil[1]{Anhui Jianzhu University}%
\affil[2]{Anhui Jianzhu University South Campus}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
Nowadays, with the development of the times, network structure analysis
has become a hot issue in some fields. The eigenvalues of normalized
Laplacian are very important for some network structure properties. Let
Qn be octagonal-quadrilateral networks composed of n octagons and n
squares and let Q2n be the strong prism of Qn. The strong product of a
complete graph of order 2 and a complete graph of order G forms a strong
prism of the graph G. In this paper, the decomposition theorem of the
associated matrix is used to completely investigate the normalized
Laplacian spectrum of Qn2. In addition, we establish exact formulas for
the degree-Kirchhoff index and the number of spanning trees of Qn2.%
\end{abstract}%



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