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The Kirchhoff index of graphs, introduced by Klein and Randi\'{c} in 1993,has been known useful in the study of computer science, complex network andquantum chemistry. The Kirchhoff index of a graph $G$ is defined as$Kf(G)=\sum\limits_{\{u,v\}\subseteq V(G)}\Omega_{G}(u,v)$, where$\Omega_{G}(u,v)$ denotes the resistance distance between $u$ and $v$ in $G$.  In this paper, we determine the maximum (resp. minimum) $k$-polycyclic chainswith respect to Kirchhoff index for $k\geq 5$, which extends the results ofYang and Klein [Comparison theorems on resistance distances and Kirchhoffindices of $S,T$-isomers, Discrete Appl. Math. 175 (2014) 87-93], Yang and Sun[Minimal hexagonal chains with respect to the Kirchhoff index, Discrete Math.345 (2022) 113099], Sun and Yang [Extremal pentagonal chains with respect tothe Kirchhoff index, Appl. Math. Comput. 437 (2023) 127534] and Ma [Extremaloctagonal chains with respect to the Kirchhoff index, arXiv: 2209.10264].

Extremal Kirchhoff index in polycyclic chains