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

Abstract

A generated n-sequence of fuzzy topographic topological mapping, ${\text{FTTM}}_n$ , 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 ${\text{FTTM}}_n$ and establish their relations to the Hamiltonian polygonal paths. Finally, the relation between the Hamiltonian polygonal paths induced from ${\text{FTTM}}_n$ to the k-Fibonacci sequence is established and their upper and lower bounds’ number of paths is determined.