  The degree-Kirchhoff index of a graph is given by the sum of inverses of
non-zero eigenvalues of the normalized Laplacian matrix of the graph multiplied
with the total degree of the graph. Explicit formulas for the degree-Kirchhoff
index of various types of cylinder chain and M\"{o}bius chain have been
obtained by many researchers in the recent past. In the present paper, we
obtain closed-form formulas for the degree-Kirchhoff index of pentagonal
cylinder/ M\"{o}bius chain. Also we find here the Gutman index and the Schultz
index for those graphs.
