Linear prime labeling of a graph is the labeling of the vertices with {0,1,2---,p-1} and the direct edges with twice the value of the terminal vertex plus value of the initial vertex. The greatest common incidence number of a vertex (gcin) of in degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of in degree greater than one is one, then the graph admits linear prime labeling. Here we investigated some direct cycle related graphs for linear prime labeling.