Given a distribution \(D\) of pebbles on the vertices of a graph \(G\), a pebbling move consists of removing two pebbles from a vertex and placing one on an adjacent vertex (the other is discarded). The pebbling number of a graph, denoted by \(f(G)\), is the minimal integer \(k\) such that any distribution of \(k\) pebbles on \(G\) allows one pebble to be moved to any specified vertex by a sequence of pebbling moves. In this paper, we calculate the pebbling number of the graph \(D_{n,C_m}\) and consider the relationship the pebbling number between the graph \(D_{n,C_m}\) and the subgraphs of \(D_{n,C_m}\).