HybridHAM: A Novel Hybrid Heuristic for Finding Hamiltonian Cycle

Table 1

Vertex selection criteria.

Vertex Selection Rule	Step	Reason
Selection of Highest degree initial vertex.	Step 1	It increases the probability of getting a path to reach back to this vertex to form the cycle.
Greedy selection of smallest degree vertices during path construction.	Step 1	Giving preference to smaller degree vertices increases the probability of longer paths. For example, if the degree of a vertex adjacent to the current end vertex of the path is two, then it should be included first in the path, as it is the only possible position of the vertex in the Hamiltonian path.
Selection of the highest degree end of the initial path for rotational transformation	Step 2	It increases the probability for getting a new end vertex for extending the path further to create a Hamiltonian path
Selection of the smallest degree end vertex for rotational transformation	Step 3	This is done to keep the highest degree end vertex, since the probability of getting an edge connecting a higher degree vertex is more compared to a smaller degree vertex.