New Sufficient Conditions for Some Hamiltonian Properities of Graphs

For a connected graph \(G = (V, E)\), its inverse degree is defined as
\(\sum_{v\in V} \frac{1}{d(v)}\). Using an upper bound for the inverse degree of a graph obtained by Cioaba in [6], in this note, we present new sufficient conditions for some Hamiltonian properties of graphs.