An implicit degree condition for hamiltonian graphs

In 1980, Bondy generalized known Ore’s theorem by proving that a k -connected graph of order n is hamiltonian if a degree sum of any k + 1 independent vertices is greater than ( 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].