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The polygonal cylinder Cm,n is a graph obtained from Cartesian product of paths Pm and Pn and using topological identification of vertices and edges of two opposite sides Pm×Pn. We have redefined the polygonal cylinder Cm,n by using Cartesian product of Cm−1×Pn. In this paper, we have introduced a closed polygonal cylinder C[m,n], is a graph obtained from Cartesian product of cycle Cm and Pn. Further more we have obtained first and second Zagreb, F-index, first and second hyper-Zagreb, harmonic, Randić, sum-connectivity and atom-bond connectivity indices of polygonal cylinder and closed polygonal cylinder of a graph.

Some degree based connectivity indices of the polygonal cylinders of a graph