Let denote the implicit degree of a vertex in a graph . We define to be implicit claw-heavy if every induced claw of has a pair of nonadjacent vertices such that their implicit degree sum is more than or equal to . In this paper, we show that an implicit claw-heavy graph is hamiltonian if we impose certain additional conditions on involving numbers of common neighbors of some specific pair of nonadjacent vertices, or forbidden induced subgraphs. Our results extend two previous theorems of Chen et al. [B. Chen, 8. Zhang and S. Qiao, Hamilton cycles in claw-heavy graphs, Discrete Math., on the existence of Hamilton cycles in claw-heavy graphs.
