The multiplicative degree-Kirchhoff index and complexity of a class of linear networks

In this paper, we focus on the strong product of the pentagonal networks. Let $R_n$ be a pentagonal network composed of $2n$ pentagons and $n$ quadrilaterals. Let $P_n^2$ denote the graph formed by the strong product of $R_n$ and its copy $R_n^{\mathrm{\prime }}$. By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of $P_n^2$ is determined.