Enumeration of Perfect Matching Dominating Cycles in Certain Class of Graphs

In this paper, we have found the number of distinct perfect matching dominating cycles for complete, complete bipartite, Petersen's and Wheel graphs. For a particular choice of perfect matching, the number is found for the hypercube graph. Since the necessary and sufficient condition for the existence of perfect matching dominating cycles is that the perfect matching minor is Hamiltonian, the number of distinct perfect matching dominating cycles is found by counting the number of distinct Hamilton cycles in the perfect matching minor.