The Kirchhoff index is defined as the sum of resistance distances between all
pairs of vertices in a graph. This index is a critical parameter for measuring
graph structures. In this paper, we characterize polygonal chains with the
minimum Kirchhoff index, and characterize even (odd) polygonal chains with the
maximum Kirchhoff index, which extends the results of \cite{45}, \cite{14} and
\cite{2,13,44} to a more general case.Comment: 13 pages. arXiv admin note: substantial text overlap with
  arXiv:2209.1026