The hamiltonian cycle for the cases m = 10 and m = 11 are shown in the Figures 2.

For any k [greater than or equal to] 6, the hamiltonian cycle of [P.

For any k [greater than or equal to] 6, the hamiltonian cycle on 2k vertices can be constructed by inserting a copies of subgraph of Figure 2.

If the degree sum of any two nonadjacent vertices is at least n, then G has a

Hamiltonian Cycle.

A Hamiltonian cycle over distance is the ordering of housing sale coordinates such that the sum of differenced distances is minimized.

2) The Hamiltonian cycle is the solution to the famous Traveling Salesman Problem (TSP).

In this paper we prove that a through-vertex Hamiltonian cycle exists in any triangular or tetrahedral grid under very mild conditions, and that there exist quadrilateral and hexahedral grids for which no unconstrained Hamiltonian path exists.

A Hamiltonian cycle is a cycle in which every element in G appears exactly once except for [E.

This special type of path is called a Hamiltonian cycle.

All she can verify is that a Hamiltonian cycle exists.

To determine the Hamiltonian circuit it self is a NP-complete problem and when shortest distance and minimum time is added with the Hamiltonian Cycle, it becomes a very hard optimization problem in the field of operations research.

For each chromosome Chromo[N] there must be a Hamiltonian cycle.