Graph of Fuzzy Topographic Topological Mapping in relation to k-Fibonacci Sequence

Abstract

A generated n-sequence of fuzzy topographic topological mapping, FTTMn, is a combination of n number of FTTM’s graphs. An assembly graph is a graph whereby its vertices have valency of one or four. A Hamiltonian path is a path that visits every vertex of the graph exactly once. In this paper, we prove that assembly graphs exist in FTTMn and establish their relations to the Hamiltonian polygonal paths. Finally, the relation between the Hamiltonian polygonal paths induced from FTTMn to the k-Fibonacci sequence is established and their upper and lower bounds’ number of paths is determined.