An implicit degree condition for hamiltonian graphs

In 1980, Bondy generalized known Ore’s theorem by proving that a kk-connected graph of order nn is hamiltonian if a degree sum of any k+1k+1 independent vertices is greater than (k+1)(n−1)/2(k+1)(n−1)/2. In this work, we generalize this result replacing the degree sum by the implicit degree sum. A concept of the implicit degree was introduced by Zhu et al. in 1989 [5].