A pancake graph was proposed as a topology for interconnection networks of parallel computers, and it has a merit that it can connect many nodes with small diameter and small degree. However, the number of nodes in a pancake graph must be equal to the factorial of an integer, which causes a demerit that it lacks incremental expandability. Hence, in this paper, we propose a graph, an incomplete pancake graph, that is obtained by deleting some of sub graphs of a pancake graph, and we give algorithms for the problems of the simple routing, the Hamiltonian cycle, the Hamiltonian path, and the container in incomplete pancake graphs.