Academy & Industry Research Collaboration Center
The authors consider finite and simple graphs in this paper; undefined notations and terminology can be found in. A hamiltonian graph is a graph with a spanning cycle, also called a hamiltonian cycle. They note that the spanning cycle is not unique. Now suppose that E' is a nonempty subset of E. The sub graph of G where vertex set is the set of ends of edges in E' and whose edge set is E' is called the sub graph of G induced by E' and is denoted by G[E']; G[E'] is an edge induced sub graph of G.