What is Cycle in a Network

A cycle passing through all the vertices exactly once in a graph is a Hamiltonian cycle (HC). In the field of network system, HC plays a vital role as it covers all the vertices in the system. If uncertainty exists on the vertices and edges, then that can be solved by considering fuzzy Hamiltonian cycle. Further, if indeterminacy also exist, then that issue can be dealt efficiently by having neutrosophic Hamiltonian cycle. In computer science applications, objects may not be a crisp one as it has uncertainty and indeterminacy in nature. Hence, new algorithms have been designed to find interval neutrosophic Hamiltonian cycle using adjacency matrix and the minimum degree of a vertex. This chapter also applied the proposed concept in a network system.