New Sufficient Conditions for Some Hamiltonian Properities of Graphs

Abstract

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.