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The degree-Kirchhoff index of a graph is given by the sum of inverses ofnon-zero eigenvalues of the normalized Laplacian matrix of the graph multipliedwith the total degree of the graph. Explicit formulas for the degree-Kirchhoffindex of various types of cylinder chain and M\"{o}bius chain have beenobtained by many researchers in the recent past. In the present paper, weobtain closed-form formulas for the degree-Kirchhoff index of pentagonalcylinder/ M\"{o}bius chain. Also we find here the Gutman index and the Schultzindex for those graphs.

On the degree-Kirchhoff index, Gutman index and the Schultz index of pentagonal cylinder/ M\"{o}bius chain