Hamiltonian polygonal path in assembly graph of FTTM

Fuzzy Topographic Topological Mapping (FTTM) consists of four topological spaces that are homeomorphic to each other. A sequence of FTTMn is a combination of n terms of FTTM. An assembly graph is a graph with all vertices have valency of one or four. A Hamiltonian path is a path that visits every vertices of a graph exactly once. In this paper, we prove an assembly graphs exists in FTTMn and relation between the Hamiltonian polygonal paths and assembly graph of FTTMn. Several definitions and theorems are developed for the purpose.