The minimum number of Hamilton cycles in a Hamiltonian threshold graph of a prescribed order
Pu Qiao, Xingzhi Zhan · Journal of Graph Theory · 2019
Abstract We prove that the minimum number of Hamilton cycles in a Hamiltonian threshold graph of order is and this minimum number is attained uniquely by the graph with degree sequence of distinct degrees. This graph is also the unique graph of minimum size among all Hamiltonian threshold graphs of order .